Coordinated Multipoint Transmission and Reception (CoMP)

ABSTRACT

A wireless communications method implemented in a network system that supports coordinated multipoint transmission and reception (CoMP) is disclosed. The wireless communications method includes informing a user equipment (UE) semi-statically of a codebook subset for each channel state information (CSI) process, wherein the UE is restricted to report an indication of a precoding matrix within the codebook subset. Other methods, apparatuses, and systems are also disclosed.

This application is a divisional of co-pending U.S. patent applicationSer. No. 13/948,388, entitled “Coordinated Multipoint Transmission andReception (CoMP),” filed Jul. 23, 2013, which in turn claims the benefitof U.S. Provisional Application No. 61/675,541, entitled “CoordinatedMulti-Point Transmission and Reception in Heterogenous Networks:Approximation Algorithms and System Evaluation,” filed on Jul. 25, 2012,U.S. Provisional Application No. 61/706,301, entitled “ResourceAllocation Schemes for Heterogeneous Networks,” filed on Sep. 27, 2012,U.S. Provisional Application No. 61/678,882, entitled “CSI Feedback andPDSCH Mapping for Coordinated Multipoint Transmission and Reception,”filed on Aug. 2, 2012, U.S. Provisional Application No. 61/683,263,entitled “PDSCH Mapping in Coordinated Multipoint Transmission andReception (CoMP),” filed on Aug. 15, 2012, and U.S. ProvisionalApplication No. 61/706,752, entitled “PDSCH mapping for CoordinatedMultipoint Transmission and Reception (CoMP),” filed on Sep. 27, 2012,the contents of all of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates to coordinated multiple point transmissionand reception (CoMP) and more particularly to channel state information(CSI) feedback, physical downlink shared channel (PDSCH) mapping,resource allocation, and some other features for CoMP.

In this document, we investigate the channel state information (CSI)feedback and the resource mapping for cooperative communication orspecifically, coordinated multipoint transmission and reception (CoMP)which is now in discussion for release-11 3GPP standardization. Inparticular, we first present a CSI feedback framework with bettertradeoff between the performance and the feedback overhead. It has beenagreed that three CoMP transmission schemes, namely, joint transmission(JT) or joint processing (JP), coordinated scheduling or beamforming(CS/CB), and dynamic point selection (DPS), are supported in the new3GPP cellular system. To support all possible CoMP transmission schemes,we proposed the CSI feedback schemes based on the size of measurementset which is configured by the network and signalled to the userterminal or user equipment (UE). Then we provide the resource mappingsolutions for the problems related to different cell-specific referencesignal (CRS) in different cells and consequently the collision betweenthe CRS and the data sent on the physical downlink shared channel(PDSCH). We also address the PDSCH mapping to solve the mismatch of thePDSCH starting points due to the different size of orthogonal frequencydivision multiplexing (OFDM) symbols allocated for the physical downlinkcontrol channel (PDCCH) transmission.

REFERENCES

-   [1] 3GPP, “Final Report of 3GPP TSG RAN WG1 #66bis v1.1.0,” 3GPP TSG    RAN WG1 R1-114352.-   [2] 3GPP, “Draft Report of 3GPP TSG RAN WG1 #67 v0.1.0”.-   [3] 3GPP, “Evolved Universal Terrestrial Radio Access (E-UTRA);    Physical channels and modulation. TS 36.211 V10.1.0”.-   [4] NTT DoCoMo, “Investigation of specification impact for Re1.11    CoMP” 3GPP TSG RAN WG1 R1-112600 Meeting#66, Athens, Greece, August    2011.-   [5] 3GPP, “Evolved Universal Terrestrial Radio Access (E-UTRA);    Physical layer procedures. TS 36.211 V10.1.0”.-   [6] TR36.819, “Coordinated multi-point operation for LTE physical    layer aspects”, 3GPP, v11.1.0.-   [7] RP-111365 “Coordinated Multi-Point Operation for LTE”, 3GPP TSG    RAN-P #53.-   [8] NEC Group, “PDSCH mapping issues in CoMP” 3GPP TSG RAN WG1    Meeting#69, R1-122603, Prague, Czech, May 2012.-   [9] Ericsson, “Control Signaling in Support of CoMP” 3GPP TSG RAN    WG1 R1-122843 Meeting#69, Prague, Czech, May 2012.-   [10] Intel, “Views on CRS/PDSCH RE Collision in Joint Transmission”,    3GPP TSG RAN WG1 R1-122655 Meeting#69, Prague, Czech, May 2012.

BRIEF SUMMARY OF THE INVENTION

An objective of the present invention is to provide efficient CSIfeedback, PDSCH RE mapping, and resource allocation for CoMP.

An aspect of the present invention includes a communications methodimplemented in a transmission point (TP) used in a coordinatedmultipoint transmission and reception (CoMP) system. The communicationsmethod includes transmitting, to a user equipment (UE), an indication ofa channel state information (CSI) process in a CSI pattern comprising aset of CSI processes, wherein the UE is configured with the CSI processfor at least one of the other CSI processes in the CSI pattern, andwherein a reported rank indication (RI) for the CSI process is the sameas an RI for said at least one of the other CSI processes.

Another aspect of the present invention includes a communications methodimplemented in a user equipment (UE) used in a coordinated multipointtransmission and reception (CoMP) system. The communications methodincludes receiving, from a transmission point (TP), an indication of achannel state information (CSI) process in a CSI pattern comprising aset of CSI processes, wherein the UE is configured with the CSI processfor at least one of the other CSI processes in the CSI pattern, andwherein a reported rank indication (RI) for the CSI process is the sameas an RI for said at least one of the other CSI processes.

Still another aspect of the present invention includes a communicationsmethod implemented in a coordinated multipoint transmission andreception (CoMP) system. The communications method includes indicating,to a user equipment (UE), a channel state information (CSI) process in aCSI pattern comprising a set of CSI processes, configuring the UE withthe CSI process for at least one of the other CSI processes in the CSIpattern, and reporting, from the UE, a rank indication (RI) for the CSIprocess that is the same as an RI for said at least one of the other CSIprocesses.

Still another aspect of the present invention includes a transmissionpoint (TP) used in a coordinated multipoint transmission and reception(CoMP) system. The TP includes transmitter to transmit, to a userequipment (UE), an indication of a channel state information (CSI)process in a CSI pattern comprising a set of CSI processes, wherein theUE is configured with the CSI process for at least one of the other CSIprocesses in the CSI pattern, and wherein a reported rank indication(RI) for the CSI process is the same as an RI for said at least one ofthe other CSI processes.

Still another aspect of the present invention includes a user equipment(UE) used in a coordinated multipoint transmission and reception (CoMP)system. The user equipment includes a receiver to receive, from atransmission point (TP), an indication of a channel state information(CSI) process in a CSI pattern comprising a set of CSI processes,wherein the UE is configured with the CSI process for at least one ofthe other CSI processes in the CSI pattern, and wherein a reported rankindication (RI) for the CSI process is the same as an RI for said atleast one of the other CSI processes.

Still another aspect of the present invention includes a coordinatedmultipoint transmission and reception (CoMP) system including a userequipment (UE), and a transmission point (TP) to transmit, to the UE, anindication of a channel state information (CSI) process in a CSI patterncomprising a set of CSI processes, wherein the UE is configured with theCSI process for at least one of the other CSI processes in the CSIpattern, and wherein a reported rank indication (RI) for the CSI processis the same as an RI for said at least one of the other CSI processes.

Still another aspect of the present invention includes a communicationsmethod implemented in a transmission point (TP) used in a coordinatedmultipoint transmission and reception (CoMP) system. The communicationsmethod comprises transmitting, to a user equipment (UE), attributers forup to four indicators indicating at least physical downlink sharedchannel (PDSCH) resource element (RE) mapping, and transmitting, to theUE, one of the four indicators, each of which is conveyed in 2 bits,wherein the four indicators comprises ‘00’, ‘01’, ‘10’, and ‘11’corresponding to a first set, a second set, a third set, and a fourthset of parameters, respectively.

Still another aspect of the present invention includes a communicationsmethod implemented in a user equipment (UE) used in a coordinatedmultipoint transmission and reception (CoMP) system. The communicationsmethod comprises receiving, from a transmission point (TP), attributersfor up to four indicators indicating at least physical downlink sharedchannel (PDSCH) resource element (RE) mapping, and receiving, from theTP, one of the four indicators, each of which is conveyed in 2 bits,wherein the four indicators comprises ‘00’, ‘01’, ‘10’, and ‘11’corresponding to a first set, a second set, a third set, and a fourthset of parameters, respectively.

Still another aspect of the present invention includes a communicationsmethod implemented in a coordinated multipoint transmission andreception (CoMP) system. The communications method comprisestransmitting, from a transmission point (TP) to a user equipment (UE),attributers for up to four indicators indicating at least physicaldownlink shared channel (PDSCH) resource element (RE) mapping, andtransmitting, from the TP to the UE, one of the four indicators, each ofwhich is conveyed in 2 bits, wherein the four indicators comprises ‘00’,‘01’, ‘10’, and ‘11’ corresponding to a first set, a second set, a thirdset, and a fourth set of parameters, respectively.

Still another aspect of the present invention includes a transmissionpoint (TP) used in a coordinated multipoint transmission and reception(CoMP) system. The transmission point comprises a first transmitter totransmit, to a user equipment (UE), attributers for up to fourindicators indicating at least physical downlink shared channel (PDSCH)resource element (RE) mapping, and a second transmitter to transmit, tothe UE, one of the four indicators, each of which is conveyed in 2 bits,wherein the four indicators comprises ‘00’, ‘01’, ‘10’, and ‘11’corresponding to a first set, a second set, a third set, and a fourthset of parameters, respectively.

Still another aspect of the present invention includes a user equipment(UE) used in a coordinated multipoint transmission and reception (CoMP)system. The user equipment comprises a first receiver to receive, from atransmission point (TP), attributers for up to four indicatorsindicating at least physical downlink shared channel (PDSCH) resourceelement (RE) mapping, and a second receiver to receive, from the TP, oneof the four indicators, each of which is conveyed in 2 bits, wherein thefour indicators comprises ‘00’, ‘01’, ‘10’, and ‘11’ corresponding to afirst set, a second set, a third set, and a fourth set of parameters,respectively.

Still another aspect of the present invention includes a coordinatedmultipoint transmission and reception (CoMP) system comprising a userequipment (UE), and a transmission point (TP) to transmit, to a userequipment (UE), attributers for up to four indicators indicating atleast physical downlink shared channel (PDSCH) resource element (RE)mapping, wherein the UE receives, from the TP, one of the fourindicators, each of which is conveyed in 2 bits, and wherein the fourindicators comprises ‘00’, ‘01’, ‘10’, and ‘11’ corresponding to a firstset, a second set, a third set, and a fourth set of parameters,respectively.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a homogenous CoMP network with M=3 macrocell BSs.

FIG. 2 depicts a heterogenous CoMP network with M=3 macrocell BSs.

FIG. 3 depicts an example of CRS/PDSCH collisions for two TPs withdifferent cell IDs. Both TPs have two CRS antenna ports.

FIG. 4 depicts an example of CRS/PDSCH collisions for the TPs with thesame cell IDs but different number of CRS antenna ports. One TP (left)has two CRS antenna ports and the other (right) has four antenna ports.

FIG. 5 depicts an example of PDSCH starting point mismatch for the TPswith different cell IDs.

FIG. 6 depicts resource mapping for CRS/PDSCH collision avoidance. Left:the resource mapping for the example in FIG. 3. Right: the resourcemapping for the example in FIG. 4.

FIG. 7 depicts data symbol allocations for CRS/PDSCH collisionavoidance. Left: Original data symbol allocation assuming the serving TPsingle cell transmissions. Right: Data symbol allocations for CoMPtransmissions (JT or DPS) with CRS/PDSCH collision avoidance, method 1.

FIG. 8 depicts data symbol allocations for CRS/PDSCH collisionavoidance. Left: Original data symbol allocation assuming the serving TPsingle cell transmissions. Right: Data symbol allocations for CoMPtransmissions (JT or DPS) with CRS/PDSCH collision avoidance, method 2.

FIG. 9 depicts BLER performance of a rate-½ LTE turbo code withpuncturing (muting) and/or dirty received bits.

FIG. 10 depicts BLER performance of a rate-½ LTE turbo code withpuncturing (muting) and partial data with stronger noise.

DETAILED DESCRIPTION 1 System Description

We consider a cluster which consists of M transmission points (TPs).Each TP can be either a macro-cell base station (BS) or a low powerremote radio head (RRH). Therefore, the CoMP network could be ahomogeneous network consisting of all macro-cell BSs, i.e., homogeneousnetwork, as shown in FIG. 1 or a heterogeneous network (HetNet) which ismixture of macro-cell BSs and lower power RRHs as shown in FIG. 2. Thereceived signal for the target user equipment (UE) at a resource element(RE) over which data is transmitted to that UE, is given by

$\begin{matrix}{y = {{\sum\limits_{i = 1}^{M}\; {\sqrt{\frac{\rho_{i}}{r_{i}}}H_{i}W_{i}s_{i}}} + {\overset{\sim}{H}\overset{\sim}{W}\overset{\sim}{s}} + {n.}}} & (1)\end{matrix}$

where H_(i), i=1, . . . , M denotes the channel seen by the UE from theith transmission point in its CoMP set, where the composition of thelatter set is decided in a semi-static manner by the network controllerbased on long-term signal-to-interference-plus-noise (SINR) ratiomeasurements and is held fixed across many sub-frames; ρ_(i) is thetransmission power or energy per resource element (EPRE) used by the ithtransmission point; W_(i) and s_(i) are the precoding matrix (with r_(i)columns) and the data symbol vector transmitted by the ith transmissionpoint; {tilde over (H)}, {tilde over (W)}, and {tilde over (s)} are thecomposite channel matrix, precoding matrix, and data symbol vectortransmitted by all the other transmission points outside the UE's CoMPset. Then, if the UE receives a data stream sent only along the jthlayer of the mth transmission point, received SINR corresponding to thatstream at the UE is given by

$\begin{matrix}{{\gamma_{mj} = \frac{\frac{\rho_{m}}{r_{m}}F_{mj}^{\dagger}H_{m}W_{mj}W_{mj}^{\dagger}H_{m}^{\dagger}F_{mj}}{\begin{matrix}{{{F_{mj}^{\dagger}( {{\frac{\rho_{m}}{r_{m}}\Sigma_{j^{\prime},{j^{\prime} \neq j}}H_{m}W_{{mj}^{\prime}}W_{{mj}^{\prime}}^{\dagger}H_{m}^{\dagger}} + {\Sigma_{i \neq m}\frac{\rho_{i}}{r_{i}}H_{i}W_{i}W_{i}^{\dagger}H_{i}^{\dagger}}} )}F_{mj}} +} \\{F_{mj}^{\dagger}{RF}_{mj}}\end{matrix}}},} & (2)\end{matrix}$

where F_(mj) is the receive filter to retrieve signal s_(mj) from thejth layer of the mth transmission point and R is the covariance of theinterference outside CoMP set plus noise, i.e., R={tilde over (H)}{tildeover (W)}{tilde over (W)}†{tilde over (H)}†+I. The correspondinginformation rate is then

η_(mj)=log(1+γ_(mj))  (3)

Without loss of generality, we assume the transmission point 1 is theserving cell that is supposed to send the data symbols to the UE forconventional single cell transmission (without CoMP) as well as thecontrol signaling and is the TP to which the UE reports its CSI feedbackon the uplink channel. Therefore without CoMP, the SINR is γ_(1j), jεS₁,where S₁ is the set of layers intended for this UE. The total rate forthe UE of interest is then given by η₁=Σ_(jεS) ₁ η_(1j). We note thatall CSI can be passed to the network controller in a CoMP network whichthen does the scheduling.

For CS/CB CoMP transmission scheme, the data is still transmitted fromthe serving cell (or equivalently the anchor cell where the controlsignalling is received from). Although the SINR is still γ_(1j) as givenin (2) (with m=1), transmit precoding matrices W_(i), i=1, . . . , M arejointly optimized so that the interference from the intra-CoMP set isreduced.

For DPS scheme, based on the CSI feedback from all UEs, the networkcontroller selects the transmission points for each UE so that theweighted sum rate of the system is maximized. Assume that m* is thetransmission point selected by the network controller for the UE. TheSINR corresponding to the j^(th) layer is then γ_(m*j) and thetransmission rate is then η_(m*j).

On the other hand in the JT scheme, the same data symbols aretransmitted through multiple, say M_(JT) transmission points in the CoMPset. Denote the set of transmission points for JT as ν, where ν⊂{1, . .. , M} and let its complement set be denoted by ν. For conveniencesuppose that all TPs in ν serve only the UE of interest over theresource block. Then, we can rewrite the signal model in (1) as

$\begin{matrix}{{y = {{\underset{i \in V}{\Sigma}\sqrt{\frac{\rho_{i}}{r_{i}}}H_{i}W_{i}^{j\; \phi_{i}}s} + {\underset{i \in \overset{\_}{V}}{\Sigma}\sqrt{\frac{\rho_{i}}{r_{i}}}H_{i}W_{i}s_{i}} + {\overset{\sim}{H}\overset{\sim}{W}\overset{\sim}{s}} + n}},} & (4)\end{matrix}$

where φ_(i) is the coherent phase adjustment to improve the SINR forcoherent JT. We assume that the serving cell BS with index 1 is alwayspresent in ν for the JT. We then fix φ₁=0. In non-coherent JT, we do notneed the feedback on φ_(i), i.e., φ_(i)=0∀iεν is applied. We can see forJT, a common transmission rank r is employed for all W_(i)iεν. Define

$H_{V}\overset{\Delta}{=}{\Sigma_{i \in V}\sqrt{\frac{\rho_{i}}{r_{i}}}H_{i}W_{i}{^{j\; \phi_{i}}.}}$

The SINR for the j^(th) layer is then given by

$\begin{matrix}{{\gamma_{V,j} = \frac{F_{V,j}^{\dagger}H_{V,j}H_{V,j}^{\dagger}F_{V,j}}{\begin{matrix}{{{F_{V,j}^{\dagger}( {{\Sigma_{j^{\prime},{j^{\prime} \neq j}}H_{V,j^{\prime}}H_{V,j^{\prime}}^{\dagger}} + {\Sigma_{i \in \overset{\_}{V}}\frac{\rho_{i}}{r_{i}}H_{i}W_{i}W_{i}^{\dagger}H_{i}^{\dagger}}} )}F_{V,j}} +} \\{F_{V,j}^{\dagger}{RF}_{V,j}}\end{matrix}}},} & (5)\end{matrix}$

where F_(ν) denotes the receiver filter on the signal in (4) for CoMP JTtransmissions. The corresponding rate for the CoMP JT transmission isthen η_(ν)=Σ_(j=1) ^(r) log(1+γ_(ν,j)).

2 CSI Feedback for CoMP

We now consider the CSI feedback for CoMP schemes. To support all agreedCoMP transmission schemes including JT, CS/CB, and DPS, a general CSIfeedback framework has been discussed during the last several 3GPP-RAN1meetings. From at-least one port of each transmission point in the CoMPset, a reference signal (RS) is sent in one or more resource elements(whose positions are conveyed by the network in advance to the UE) inorder to let UE estimate the channel from that port of that TP. LetH_(i) be the channel matrix estimated by the UE, corresponding to allsuch ports of the ith TP. In release-10 and earlier legacy systems, animplicit CSI feedback is adopted such that a CSI feedback for a set ofcontiguous resource blocks (RBs) (which map to a time-frequency resourcecomprising of a set of consecutive sub-carriers and OFDM symbols)consists of a wideband preferred precoding matrix index (PMI) thatindicates a preferred precoder matrix Ĝ, a wideband rank index (RI){circumflex over (r)}, along with up-to two channel quality indices(CQIs), which are essentially quantized SINRs estimated by the UE. Asseen from Section 1 for CB/CS and DPS, such CSI feedback from the UE foreach transmission point in its CoMP set to its anchor BS is sufficientas this allows the controller to select one TP for transmission to thatUE (on each sub-band if needed) and to obtain a good SINR estimate inorder to assign an appropriate modulation and coding scheme (MCS) forthe UE. However, for JT, aggregated SINR (CQI) feedback is essential torealize the performance gain by CoMP. For coherent JT, feedback of theinter CSI-RS resource phase information is also necessary. In the sequelwe will use per-TP and per-CS-RS resource inter-changeably. In RAN1 #67meeting, the following agreement has been reached [2].

-   -   CSI feedback for CoMP uses at least per-CSI-RS-resource        feedback.        However the contents of this per-CSI-RS-resource feedback have        not yet been decided.

Based on this agreement, we now provide efficient approaches for CoMPCSI feedback. We first discuss the alternative solutions for per CSI-RSresource feedback either with or without the common rank restriction,and moreover, the options for inter-CSI-RS-resource feedback. Later wepropose a best-{hacek over (M)} CSI feedback scheme for CoMP.

2.1 Per CSI-RS Resource Feedback without Common Rank Restriction

Since per-CSI-RS-feedback has been agreed to be mandatory for all CoMPtransmission schemes, it raises an issue on the rank feedback for eachtransmission point. Whether or not to enforce a common rank feedback forall the transmission points in the CoMP set is yet to be decided. Wefirst discuss the pros/cons on the per-CSI-RS-feedback based feedbackscheme for CoMP, without the common rank restriction and provide oursolutions.

With per CSI-RS resource feedback, each UE sends the CSI feedback foreach transmission point in its CoMP set, which is computed assumingsingle-point transmission hypothesis. Therefore, it is possible thatpreferred rank varies in the CSI feedback computed for differenttransmission points. In this option, the UE is allowed to send the bestrank for each transmission point along with corresponding PMI/CQIs tothe BS.

For CS/CB and DPS CoMP transmission schemes, the transmission to the UE(if it is scheduled) is performed from one transmission point in itsCoMP set (on each of its assigned RBs) which corresponds to one CSI-RSresource. For wideband DPS (henceforth referred to as DPS-w) each UE isserved by one TP on all its assigned RBs, whereas for subband DPS(DPS-s) the UE can be served by a different TP on each assigned RB.Then, for DPS-w a higher CoMP performance gain can be achieved withoutcommon rank restriction as the CSI feedback for each TP computed using apreferred rank is available to the controller. Next, supposing that theCSI-RS feedback is determined based on the assumption that the other TPsin the CoMP set are silent (or muted), the interference from other TPsin the aftermath of scheduling can be approximated by the controllerusing CSI-RS resource feedback corresponding to the other TPs. Further,even with different assumptions on the interference from other TPs whichwill be discussed later, the controller can estimate the post-schedulingSINR for the selected TP reasonably well. Thus, per-CSI-RS-resourcefeedback without common rank seems suitable for DPS-w. Similarly forCS/CB, where each UE is served data only by its pre-determined anchor orserving cell TP, there is no significant performance degradation sinceeach UE reports more accurate CSI for other transmission points usingthe respective preferred ranks. This option also facilitates thefallback from CoMP to non-CoMP single-cell transmissions.

However, for JT enforcing the common per-UE transmission rank willnecessitate rank-override when the UE reports different ranks fordifferent transmission points in its CoMP set. Further in this case,another important issue is the mechanism to send the inter-CSI-RSresource feedback or aggregated feedback across multiple CSI-RSresources when there is no common rank restriction.

To accommodate CoMP JT scheme, we now provide the following solution forthe case without common feedback rank restriction.

-   Solution 1: If preferred ranks for different CSI-RS resources are    different, the inter-CSI-RS resource feedback or aggregated feedback    is computed based on the lowest rank among all preferred ranks.    Assume the lowest rank is {circumflex over (r)}=min{{circumflex over    (r)}_(i)}, then in each reported precoding matrix the column subset    corresponding to the {circumflex over (r)} strongest SINRs is    determined. The inter-CSI-RS resource phase feedback or aggregated    feedback is computed based on these precoding matrix column subsets    and these subsets are used to design the transmit precoder.

We consider an example with a CoMP set having two transmission points.For the cases with three or more transmission points, the resultsdiscussed below can be applied similarly. The CSI feedbacks includingpreferred precoding matrices, quantized SINRs (fedback using CQIs), andrank indices are (Ĝ₁, {circumflex over (γ)}₁, {circumflex over (r)}₁)and (Ĝ₂, {circumflex over (γ)}₂, {circumflex over (r)}₂) for thetransmission point 1 (TP1) and TP2, respectively. The UE then selectsthe rank {circumflex over (r)}=min{{circumflex over (r)}₁, {circumflexover (r)}₂}. Then the precoding matrix V₁ used in CoMP JT is assumed tobe formed using {circumflex over (r)} columns of Ĝ₁ which correspond to{circumflex over (r)} highest SINRs. If there are two or more layershaving the same SINR CQI index, a predetermined rule (known to all UEsand TPs) can be applied for column subset selection. The precodingmatrix V₂ can then be formed similarly. With the inter CST-RS resourcephase φ=[φ₁ φ₂]^(T), the composite precoding matrix is formed as

$V_{JT} = {\begin{pmatrix}{V_{1}^{j\; \phi_{1}}} \\{V_{2}^{j\; \phi_{2}}}\end{pmatrix}.}$

The inter CSI-RS resource phase feedback is determined by finding thebest φ from a predetermined set assuming the composite precoding matrixV_(JT) is employed for CoMP JT. Without loss of generality, we set φ₁=0so that only φ₂ needs to be reported.

Similarly, the aggregated SINR or aggregated CQI feedback is computedassuming that V_(JT) is employed for coherent CoMP JT or non-coherentCoMP JT with φ=[0 0]^(T).

As mentioned earlier, with Solution 1, the rank override is needed incase of JT. With Solution 1, a better DPS-w and CS/CB performance may beachieved. The performance of JT will degrade as the first few dominantright singular vectors of the composite channel are not accuratelyavailable at the controller. Moreover, common rank feedback is alsobetter suited for DPS-s since in this case a rank override isnecessitated if a UE is served by different TPs (for which it hasreported different ranks) on its different assigned RBs.

For the feedback overhead, assuming a feedback mode similar to 3-1, i.e.a wideband PMI feedback, wideband rank along with subband CQI feedback,each CSI-RS resource feedback consists of one RI (to indicate a rank sayr), and one PMI, and N min{2, r} CQIs, where N is number of subbandsthat the UE is configured to report. Thus with Solution 1, the totalfeedback for per-CSI-RS resource feedback with M CSI-RS resources isΣ_(m=1) ^(M) N min{{circumflex over (r)}_(m),2}n_(CQI)+Mn_(RI)+Mn_(PMI),where n_(CQI), n_(RI), and n_(PMI) are number of bits for each feedbackof CQI, RI and PMI, respectively. Here, we assume that a set of CQIs forN subband resources are sent back for each per-CSI-RS resource. Notethat in case of JT CoMP per-subband inter point phase and/or aggregateCQI(s) could also need to be reported. Such overhead can be reduced byimposing restrictions on CQI feedback, which we will explain later.

If the UE can report feedback for a subset of CSI-RS resources, wepropose the following solution.

-   Solution 2: The standard does not specify the common rank    restriction for per CSI-RS resource feedback. With UE centric CSI    feedback, UE decides preferred CoMP scheme. If UE prefers JT CoMP    scheme, the UE sends per-CSI-RS resource feedback with a common or    uniform rank for multiple CSI-RS resources possibly along with    aggregated CQI feedback (aggregated across all those CSI-RS    resources) and/or inter-CSI-RS resource phase feedback. If UE    prefers DPS-w or CB/CS, per-CSI-RS resource feedback is sent without    common rank restriction. Further, if the UE prefers DPS-s then it    sends per-CSI-RS resource feedback with a common rank. However, such    feedback scheme does not restrict the CoMP scheme that the    controller should use.

We can see with Solution 2, the rank override is not necessary for JTand DPS-s. Also if BS employs the CoMP scheme that the UE prefers asindicated in its CSI feedback, the system is able to achieve maximalgain with respect to that UE. Additional feedback is needed to indicatethe preferred CoMP scheme. But such feedback overhead is minimal. Notethat we have assumed a wideband indication of one preferred CoMP schemethat is common across all subbands that the UE is configured to report.This reduces the signaling overhead with negligible performancedegradation. Further, as an option to reduce overhead the system maydecide in a semi-static manner to allow only one of DPS-s and DPS-w.

The feedback overhead for Solution 2 is discussed as follows.

-   -   For JT, the total feedback overhead is min{{circumflex over        (r)},2}Nn_(CQI)+n_(RI)+Mn_(PMI), where {circumflex over (r)} is        the uniform rank selected by the UE. Additional overhead is        required for aggregated CQI feedback and/or inter-CSI-RS        resource phase feedback.    -   For CB/CS and DPS-w, the maximum overhead is Σ_(m=1) ^(M)        min{r_(m),2}Nn_(CQI)+Mn_(RI)+Mn_(PMI) which is same as that for        solution 1. However, this can be reduced since with UE centric        CSI measurement, UE may only measure the CSI for a subset of M        CSI-RS resources. In particular, for DPS, UE may only need to        feedback one CSI feedback for the anchor point and one for the        best preferred TP. Then in case of DPS-w there is one wideband        indication needed for indicating the preferred TP, whereas one        indication per subband is needed for DPS-s. Extending this        approach, we may also allow UE to only feedback CSI for the best        preferred TP (per subband for DPS-s). With this alternative,        while the overhead is reduced the scheduling gain may also        reduce since the network will be forced to use the UE preferred        TP for the transmission to this UE if it is scheduled.        Furthermore, for CB/CS the system can enforce that each user use        a specified rank in the feedback of CSI for each TP in its CoMP        set that is different from its serving TP. This reduces rank        indication overhead and may simplify UE determination of PMI for        its non-serving TPs. These specified ranks can be conveyed by        the network in a semi-static manner to the UE. Optionally, the        specified ranks can be identical for all other non-serving TPs        (for example rank-1).

To reduce the performance loss for the fallback to single-celltransmission, we also propose the following CoMP CSI feedback solutionfor JT.

-   -   The UE sends the CSI feedback for the serving TP under single TP        transmission hypothesis. For CoMP, UE also reports a wideband        PMI for each CSI-RS resource including serving TP with a uniform        rank, which can be different from the reported rank for the        single serving cell transmission, along with the aggregated CQI        for CoMP JT and/or the inter CSI-RS phase feedback.        2.2 Per CSI-RS Resource Feedback with Common Rank Restriction

We may specify the common rank restriction to ensure that a common rankis employed when the UE sends per-CSI-RS resource feedback. With commonrank restriction on per CSI-RS resource feedback, there may be aperformance degradation if DPS-w or CB/CS CoMP scheme is employed at theBS, as the preferred precoding and rank may not be the best for thetransmission point that the network eventually uses. There may also be aperformance degradation if the system falls back to the single cell(serving TP) transmission for this UE. We now propose the followingsolution based on UE centric CSI feedback that may mitigate thispossible performance loss.

-   Solution 3: The standard specifies the common rank restriction for    per CSI-RS resource feedback but does not specify which rank to use.    With UE centric CSI feedback, in case the UE prefers and indicates    JT CoMP or CS/CB the UE may send per-CSI-RS resource feedback with a    uniform rank for a subset of CSI-RS resources (possibly along with    inter-CSI-RS resource feedback and/or aggregated CQI feedback in    case of JT CoMP). With this flexibility, in case DPS-w (DPS-s) is    indicated by the UE, the UE may send the CSI feedbacks for the    serving cell and the preferred transmission point (preferred TP per    subband) with a common rank. UE can also send the CSI feedback for    only serving cell and indicate that it prefers to fall back to    single cell transmission.

With this approach, the performance degradation for DPS-w and fallingback single-cell transmission can be reduced.

As an option to reduce overhead, the system in a semi-static manner canfurther restrict the common rank to be 1 for solution 3 in case JTand/or CS-CB is preferred. The rationale is as follows. For JT, the CoMPperformance gain via coherent phase combining is achieved mostly forrank-1 transmissions. Also with common rank-1 feedback the UE only needsto feedback one aggregate CQI (per subband). For CB/CS, with rank-1channel feedback, it is easier for the coordinated BSs to control theprecoding beams for different TPs to reduce the intra CoMP setinterference.

With UE centric feedback, UE can choose the preferred CSI feedbackscheme. One simple case is that UE can choose between JT CoMP CSIfeedback with a lower rank, e.g., rank-1 feedback with aggregated CQIfeedback, or the CSI feedback for the single serving TP with higherrank, e.g., rank 2, (which has less overhead) by comparing the effectiverates it deems it can get under these two, i.e., η₁ and r_(ν), where νis the set of TPs being considered by the UE for JT. The onecorresponding to the higher rate is the type of transmission scheme(CoMP or fall-back to single serving TP) that the UE prefers and sendsthe CSI feedback accordingly. However, although this comparison is thebest approach on selecting the CSI feedback for this particular UE, itis not a good choice on the system efficiency because when UE selectsfall-back to single serving TP, the BS can schedule some datatransmissions on the other TPs. To accommodate the potentially scheduledUEs on the other TPs, we suggest the following three alternativeapproaches.

-   Alternative 1: An offset η _(i) for the ith TP is imposed and    signalled to the UE in a semi-statical manner. So the UE compares    the sum rate assuming single TP for the UE, η₁+Σ_(iεν) η _(i) and    the CoMP rate η_(ν) to select preferred transmission scheme and send    the CSI feedback accordingly. The value η _(i) can be the average    single-cell transmission rate from the TP i.-   Alternative 2: Fractional EPREs or powers {α_(i)ρ_(i)} are assumed    when the UE computes CoMP CQI so that the rate for CoMP JT computed    by UE is scaled (or equivalently for each TP i the UE scales its    effective estimated channel that includes the power ρ_(i) by a    factor √{square root over (α_(i))}). The scaling factors {α_(i)}    (which can be UE specific) can be signalled by the network to the UE    semi-statically. UE then computes CoMP SINR according to (5) but    with the scaled power α_(i)ρ_(i), iεν, and obtains the CoMP rate    η_(ν)({α_(i)ρ_(i)}). The rate comparison is between η₁ and    η_(ν)({α_(i)ρ_(i)}). With the SINR (CQI) feedback based on the    fractional powers and knowing {α_(i)}, the BS can re-scale the SINR    back for appropriate MCS assignment. Note that the role of these    {α_(i)} is to bias the UE towards making a choice. To get a finer    control each α_(i) (on a per-TP basis) can be different for    different cardinality of the set ν and/or they can be different for    different rank hypothesis.-   Alternative 3: The UE computes the rate from each transmission    point, η_(m), and compare the sum rate η₁+κΣ_(i=2) ^(M)η_(i) with    the rate of CoMP JT η_(ν), where κ is a scaling factor that can be    informed by the BS in a semi-statical manner. When κ=0, it reduces    to the original comparison between the single serving TP    transmission rate and CoMP JT rate.    2.3 Best-{hacek over (M)} CSI Feedback

Usually, the BS pre-allocates certain uplink (UL) resources for a UE tosend its CSI feedback. Since per-CSI-RS resource feedback is agreed inorder to support all CoMP schemes, a large number of UL feedbackresources have to be pre-allocated to be able to accommodate the worstcase, i.e., the highest transmission ranks for each TP along with N CQIsfor each stream (maximum 2 data stream for rank 2 or higher). Even withUE centric CSI feedback, in which the actually feedback bits can be muchless, it still could not reduce the signaling overhead since the ULfeedback resources are pre-allocated. We now propose a so-calledbest-{hacek over (M)} CSI Feedback schemes and provide two alternativeapproaches. This scheme can be applied to the systems either with orwithout the common rank restriction.

-   Alternative 1: The BS configures and semi-statically sends a signal    of {hacek over (M)} and ask the UE selects {hacek over (M)}, {hacek    over (M)}≦M, CSI-RS resources or TPs to send the CSI feedback for    each resources. The BS then pre-allocate the UL feedback channel    which is able to accommodate the CSI feedback for {hacek over (M)}    CSI-RS resources or TPs. If aggregated CQI or inter CSI-RS resource    phase feedback is specified, additional UL feedback resources for    these feedback are also allocated. UE is able to select the    preferred {hacek over (M)} TPs to send the CSI feedback accordingly.    Additional signaling on the CSI feedback corresponding to which    CSI-RS resource or TP is needed. {hacek over (M)} can be UE specific    or uniform for all UEs.

We can see that with above approach, the signalling overhead is greatlyreduced when {hacek over (M)}<M. The reason doing this is that althoughthe CoMP cluster consists of several multiple UE, for a particular UE,the number of effective coordinated TPs may be only two, or three atmost. As shown in FIG. 1, a CoMP set consists of 3 TPs. However, forUE1-UE3, there are only two effective TPs for coordination. For UE4, byselecting best {hacek over (M)}=2 of 3 coordinated TPs, there should notbe any significant performance degradation. Of course the UE can sendCSI feedback for less-than-{hacek over (M)} CSI-RS resources or TPs.

Although the above approach reduces feedback overhead significantly, theworst scenarios for CSI feedback, particularly, for the CQI feedbackshave be considered when allocating the UL feedback resources, i.e., themaximum rank for a TP or a CSI-RS resource within the CoMP set. Thisscenario is for both the case without common rank restriction and thecase with common restriction but not specifying which rank to use.Hence, we propose the following approach to further reduce unnecessaryfeedback resource allocations.

-   Alternative 2: The BS configures and semi-statically sends a signal    of {hacek over (M)} and ask the UE selects CSI-RS resources or TPs    to send the CSI feedback for total {hacek over (M)} data streams.    The BS then pre-allocate the UL feedback channel which is able to    accommodate the CSI feedback for {hacek over (M)} data streams. If    aggregated CQI or inter CSI-RS resource phase feedback is specified,    and configure additional UL feedback resources for these feedback    are also allocated. UE is able to select the preferred TPs and ranks    for each TP or the common rank for all select TPs with this {hacek    over (M)} data stream constrain.

With Alternative-2 approach, UE can select the TPs with total number ofCQI feedback sets being {hacek over (M)}. For example, the UE can sendCSI feedback for {hacek over (M)}/2 TPs if the common rank is 2 orabove, or for {hacek over (M)} TPs if the common rank is 1, or anynumber of TPs as long as Σ_(iεν) _(UE) min{r_(i), 2}≦{hacek over (M)}for the case without common rank restriction.

One variation of above alternative-2 scheme is that the restriction of{hacek over (M)} sets of CQI feedback includes the aggregated CQI. TheUE may be able to choose if aggregate CQI is needed and occupy thefeedback resources so that less per-CSI-RS resource CSI feedbacks arereported.

2.4 CoMP Feedback Format

As discussed before, with per CSI-RS resource feedback, each UE sendsthe CSI feedback for each transmission point in its CoMP set, and thisper CSI-RS resource feedback is computed assuming single-pointtransmission hypothesis (i.e., transmission only from the TPcorresponding to that CSI-RS resource). Therefore, it is possible thatpreferred rank varies in the CSI feedback computed for differenttransmission points. In this option, the UE is allowed to send the bestrank for each transmission point along with corresponding PMI/CQIs toits serving TP.

A simple way in which the network controller can control a UE's perCSI-RS resource feedback is to employ a separate codebook subsetrestriction for each TP in a UE's CoMP set (a.k.a. CoMP measurementset). In other words the controller can inform each UE in a semi-staticmanner about the codebook subset it should employ for each TP in itsCoMP set, so that the UE then searches for and reports a precoder onlyin the respective subset corresponding to each TP in its CoMP set. Thisallows the controller to tune the per CSI-RS resource feedback itreceives, for instance in case it decides that CS/CB is a morepreferable scheme it can configure the subsets corresponding to allnon-serving TPs in a UE's CoMP set to include only rank-1 precodingvectors. This allows for better quantization of dominant interferingdirections and better beam coordination which is particularly helpfulfor CS/CB.

Additionally, as an option the controller can also configure a separatemaximum rank limit on the rank that can be reported by the UE for eachTP in its CoMP set and convey these maximum rank limits to the UE in asemi-static manner. While this can be accomplished also via codebooksubset restriction, setting a separate maximum rank limit can decreasethe feedback load. For example, if a TP has four transmit antennas, withcodebook subset restriction the feedback overhead need not be decreasedsince it has to be designed to accommodate the maximal subset size,which in this case translates to six bits, two bits for rank (up-to rank4) and four bits for the PMI per rank. On the other hand, by imposing amaximum rank limit of 2, the overhead is 5 bits, one bit for rank (up-torank 2) and four bits for the PMI per rank. Note that codebook subsetrestriction can be used in conjunction with maximum rank limit.

Optionally, the network can also have the ability to semi-staticallyconfigure a separate feedback mode for each per CSI-RS resource feedbackreported by a UE. For instance the network may configure a UE to use afeedback mode for its serving-TP that allows reporting per-subband PMIand CQI(s) and a mode that allows reporting a wideband PMI withper-subband CQI(s) for some or all of the other TPs in its CoMP set.This allows the controller to reduce the overall CoMP feedback loadwithout a significant degradation in performance.

Let us denote the overall CoMP CSI feedback from a UE for a particularchoice of: per CSI-RS resource feedback modes, possible accompanyingrestrictions such as common rank report for all TPs in the CoMP set andadditional aggregate CQI(s) or inter-point phase resource(s): as a CoMPfeedback format. A key bottleneck in designing CoMP CSI feedback schemesis that the size of the UL resource used for reporting a particular CoMPfeedback format must be pre-allocated and must be designed toaccommodate the worst-case load. This is because the TP which receivesthe feedback should know the physical layer resources and attributesused for the UE feedback in order to decode it. Then, if the UE isallowed to dynamically select the feedback format from a set ofpermissible formats, the TP which receives its feedback will have toemploy blind decoding in order to jointly determine the format used bythe UE and the content within it. Such blind decoding increases thecomplexity and thus it is better to allow only a small cardinality forthe set of permissible CoMP feedback formats, say 2. Another evensimpler solution is for the controller to semi-statically configure afeedback format for a UE which then employs that format for its CSIfeedback until it is re-configured by the network.

We now provide some useful guidelines for CoMP feedback format design.

-   -   1. CoMP set size dependent feedback format: The CoMP set for a        UE is configured by the network. Thus one feedback format can be        defined for every possible CoMP set size in the CoMP cluster.        However, a simple network design also demands a small number of        feedback formats. Typical possible values of CoMP set size are:        a set size of 2 and a set size of 3. Accordingly we can define a        separate feedback format for size 2 and another one for size 3.        Additionally, as an option one other format common for all sizes        greater than 3 can be defined. Alternatively, the network can        restrict itself to configure a CoMP set for each UE which is of        size no greater than 3 and hence this additional format need not        be defined. The UE will use the format corresponding to the size        of its CoMP set. Then, each of these formats can be designed        separately and a key idea we can exploit is that for a given        feedback load, the format for a smaller set size can convey more        information about the TPs in the CoMP set.    -   2. CQI feedback in each CoMP feedback format: Note that at-least        one CQI per sub-band must be reported by the UE for each TP in        its CoMP set (or for each TP in its preferred set of TPs if the        CoMP set size is large and the UE has been configured to report        CSI for only its preferred TP set which can be any subset (of a        configured cardinality) of its CoMP set). We highlight some        approaches to configure the CQI feedback. For simplicity we        consider the case where the UE must report at-least one CQI per        sub-band for each TP in its CoMP set. The other case follows        after straightforward changes.        -   The UE can be configured to report one or at-most two CQI(s)            per sub-band for each TP in its CoMP set. Each of these            CQI(s) are computed under the assumption that the other TPs            in the CoMP set are muted so that only the outside CoMP set            interference is captured in these CQI(s). Then, the            controller can approximate the whitened downlink channel            from each TP to the user on each sub-band using the            corresponding reported PMI and CQI(s), i.e., with reference            to the model in (1) the whitened channel from the i^(th) TP            to the user is R^(−1/2)H_(i) which is approximated using the            reported PMI and CQI(s) corresponding to TP i as Ĥ_(i). The            controller can then model the signal received by the user in            the aftermath of scheduling as

$\begin{matrix}{y \approx {{\sum\limits_{i = 1}^{M}\; {{\hat{H}}_{i}x_{i}}} + {\overset{\sim}{n}.}}} & (6)\end{matrix}$

-   -   -   where ñ is the additive noise with E[ññ†]=I. Using the model            in (6) the controller can design the transmit precoders and            obtain estimates of received SINRs for each choice of            transmit precoders and choice of CoMP transmission schemes,            i.e., CS/CB or DPS or JT. This allows the controller to            select an appropriate transmission scheme. In addition to            these CQI(s), the UE can also report per sub-band “fallback”            CQI(s) for only the serving TP. These CQI(s) are computed            using the PMI reported for the serving cell after            incorporating the interference measured by the UE from TPs            outside CoMP set as well as all other TPs in the CoMP set.            Using these CQI(s) along with the PMI reported for the            serving cell, the controller can first approximate the            whitened downlink channel from the serving TP to the user on            each sub-band (the whitening is now with respect to both            intra-CoMP set and outside CoMP set interference) and then            model the signal received by the user in the aftermath of            scheduling as

y≈Ĥ ₁ ′x ₁ +ñ′,  (7)

-   -   -   where again E[ñ′ñ′†]=I. Using the model in (7) the            controller can schedule the user as a conventional            single-cell user. This allows single cell fall-back            scheduling.        -   In addition, as an option the network can also configure            each UE to report per sub-band aggregate CQI(s) where the            set of TPs from the CoMP set used by the UE to compute the            aggregate CQI(s) are configured by the network (a.k.a.            controller). Recall that the aggregate CQI(s) are computed            assuming joint transmission from a set of TPs (with the            other TPs if any in the CoMP set assumed to be silent).            While the model in (6) allows for obtaining post-scheduling            SINR estimates under JT, the SINRs so obtained need not be            accurate enough for good JT gains. The SINRs estimates            obtained using aggregate CQI(s) allow for better link            adaptation and hence larger gains via joint transmission.        -   Alternatively, instead of reporting these aggregate CQI(s)            on a per sub-band basis, they may be reported only for the            best M sub-bands (along with indices of the corresponding            sub-bands) where M is configured by the network.            Furthermore, as an option the network can also enforce that            these aggregate CQI(s) are computed as per a configurable            maximum rank limit. For example, if the network sets this            limit to one, then only one aggregate CQI is reported per            sub-band and this is computed using the best (strongest)            column from each of the PMIs that have been determined by            the UE in the per-CSI resource feedback corresponding to the            TPs over which it is computing the aggregate CQI. In case of            a higher maximum rank limit, two aggregate CQIs are reported            per sub-band and are computed using the best (strongest)            column subsets which can be determined via the procedure            described previously for CSI feedback for JT without the            common rank constraint.        -   The UE can be configured to report one or at-most two CQI(s)            per sub-band for each TP in its CoMP set. Each of these            CQI(s) are computed after incorporating the interference            measured by the UE from TPs outside CoMP set as well as all            other TPs in the CoMP set. Note that the post-scheduling            interference that the UE will see from TPs in its CoMP set            that are not serving data to it will depend on the transmit            precoders that are assigned to these TPs. Then, the            controller can also exploit its knowledge of the specific            transmit precoders that were used by the TPs in the UE's            CoMP set in the sub-frames over which the UE computed the            CQI(s). This allows the controller to modify the reported            CQIs to obtain estimates for the post-scheduling SINRs. The            modification can be done using any appropriate rule that            considers the choice of transmit precoders that the network            wants to employ and those that were used at the time of CQI            computation. Such SINR estimates can provide reasonable CoMP            gains when CS/CB or DPS is used. Notice that no additional            fall-back CQI is needed since such CQI is already reported            for the serving TP. However JT gains may be degraded due to            inaccurate link adapation. As discussed for the previous            case, as an option the UE can be configured to report            additional aggregate CQI(s) to enable JT CoMP gains. These            aggregate CQI(s) are computed assuming joint transmission            from a (configured) set of TPs incorporating the            interference from other TPs if any in the CoMP set.

We now consider some further variations that can be employed in the CoMPfeedback format design.

-   -   1. Different degrees of flexibility in the rank reports: The two        cases that have been discussed before are the one where full        flexibility is allowed in that a separate rank report (with or        without maximum rank limit) can be reported for each TP in the        CoMP set. The other one is where a common rank must be reported        for all TPs in the CoMP set. Another possibility that has a        level of flexibility in between these two options is one where a        separate rank can be reported for the serving TP along with one        other separate rank that is common for all other non-serving TPs        in the CoMP set. Furthermore, separate maximum rank limits can        be imposed on these two rank reports. Note that this option has        lower feedback compared to the full flexibility case and can        convey CSI more accurately compared to the case where a common        rank must be reported for all TPs in the CoMP set.

2.5 CoMP Feedback Formats: CoMP Measurement Set Size 2 or 3

In this section we will further specify the feedback format design byfocusing on measurement set sizes 2 and 3. In the following we willassume that each CSI-RS can be mapped to (or corresponds to) a TP. Theseprinciples can be extended in a straightforward manner to the case wherea CSI-RS corresponds to a virtual TP formed by antenna ports frommultiple TPs. Let us first consider measurement set size 2. We will listthe various alternatives in the following.

-   -   Per-point CSI-RS resource feedback for each of the two CSI-RS        resources configured for the measurement set. Each such feedback        comprises of PMI/CQI(s) computed assuming single-point        transmission hypothesis from the TP corresponding to that CSI-RS        resource with the remaining TP (corresponding to the other        CSI-RS resource) being silent, henceforth referred to as        Per-point CSI-RS resource feedback with muting. Note that the        frequency granularity of the PMI and the CQI(s) to be sent by        the user in a per-point CSI-RS resource feedback can be        separately and independently configured by the network in a        semi-static manner. For instance, the user can be configured to        send per-subband CQI(s) and wideband PMI in one per-point CSI-RS        resource feedback, while reporting per-subband CQI(s) and        per-subband PMI in the other per-point CSI-RS resource feedback.    -   Per-point CSI-RS resource feedback with muting for each of the        two CSI-RS resources. In addition, separate fallback PMI/CQI(s)        (henceforth referred to as fallback CSI) are also reported. This        fallback CSI is computed under the assumption of single-point        transmission from the serving TP and interference from all TPs        outside the CoMP set as well as interference from the other        non-serving TP in the CoMP set. For simplicity and to avoid        additional signaling overhead, the frequency granularities of        the PMI and CQI(s) in the fallback CSI can be kept identical to        those of their counterparts in the per-point CSI-RS resource        feedback with muting for the serving TP. Note that the        covariance matrix for the interference from all other TPs can be        estimated by the UE using resource elements configured for that        purpose by the network. Alternatively, the UE can be configured        by the network to estimate the covariance matrix for the        interference from outside the CoMP set using certain resource        elements. Then, the user can be made to leverage the fact that        it has already estimated the unprecoded downlink channel matrix        from the other TP in its CoMP set. Using this channel estimate        the UE can assume a scaled identity matrix to be the precoder        used by the other TP and compute the covariance matrix, which        then is added to the covariance matrix computed for outside the        CoMP set. The sum covariance matrix is then used to determine        the fallback PMI and compute the associated fall back SINRs and        fallback CQIs. Note that the scaling factor in the scaled        identity precoder can be informed to the UE in a semi-static        manner and can be based on factors such as the average traffic        load being served by the other TP (which is known to the        network). A higher scalar corresponds to a higher traffic load.        Similarly, the covariance matrix for the other TP can also be        computed by the UE assuming the precoder for the other TP to be        a scaled codeword matrix where the codeword can be uniformly        drawn from the codebook subset. The choice of subset and the        scaling factor can be conveyed to the UE by the network in a        semi-static manner.    -   Per-point CSI-RS resource feedback with muting for each of the        two CSI-RS resources. To save signaling overhead, in the        fallback CSI only fall CQI(s) are reported, where in each        subband these CQI(s) are computed using the PMI reported for the        serving TP (in the per-point CSI-RS resource feedback with        muting) corresponding to that subband and the procedure        described above. Alternatively, since the rank reported for the        serving TP under muting can be an aggressive choice for fallback        (recall that the fallback also assumes interference from the        other TP) a separate rank indicator can be allowed for fallback.        Specifically the UE can choose and indicate any rank R less than        or equal to the one reported for the serving TP under muting.        Then R columns of the PMI reported for the serving TP        (corresponding to the R highest SINRs recovered from the        associated CQI(s) under muting) are obtained. The fall back        CQI(s) are then computed using this column subset.    -   Per-point CSI-RS resource feedback with muting for each of the        two CSI-RS resources. The network can configure in a semi-static        manner the TP that the UE must assume to be the serving TP for        computing the fallback CQI(s). The remaining TP is then treated        as the interferer and the procedure described above is employed.    -   Per-point CSI-RS resource feedback with muting for each of the        two CSI-RS resources. The UE dynamically chooses the serving TP        for computing the fallback CQI(s). The remaining TP is then        treated as the interferer and the procedure described above is        employed. The choice of serving TP for computing fallback can be        configured to be the one which offers a higher rate as per the        CQI(s) computed under muting. Note that in this case the choice        is implicity conveyed to the network via the CQI(s) computed        under muting and hence need not be explicitly indicated.        Moreover, the choice can vary across subbands based on the per        subband CQI(s). However, to enable simpler fallback operation        the UE can be configured to determine a wideband choice based on        the sum rate across all subbbands so that even in this case the        choice is implicitly conveyed. Alternatively, a separate        wideband indicator can be employed to enable the UE to indicate        its choice which allows the UE to arbitrarily decide its choice        albeit on a wideband basis.    -   Per-point CSI-RS resource feedback with muting for each of the        two CSI-RS resources. A common rank constraint on the two CSI-RS        resource feedbacks is enforced so that only one rank indicator        needs to be reported. Optionally, fallback CSI as per any one of        the above listed options is also reported. Further optionally,        aggregate CQI(s) computed using the two PMIs (determined for        per-point CSI-RS resource feedback with muting) are also        reported.

Let us now consider measurement set size 3. We will list the variousalternatives in the following.

-   -   Per-point CSI-RS resource feedback for each of the three CSI-RS        resources. Each such feedback comprises of PMI/CQI(s) computed        assuming single-point transmission hypothesis from the TP        corresponding to that CSI-RS resource with the remaining TPs        (corresponding to the other two CSI-RS resources) being silent,        henceforth referred to as Per-point CSI-RS resource feedback        with muting. Note that the frequency granularity of the PMI and        the CQI(s) to be sent by the user in a per-point CSI-RS resource        feedback can be separately and independently configured by the        network in a semi-static manner. The configuration can be        different for different TPs in the user's CoMP set.    -   Per-point CSI-RS resource feedback with muting for each of the        three CSI-RS resources. In addition, separate fallback        PMI/CQI(s) (henceforth referred to as fallback CSI) are also        reported. These CQI(s) assume single-point transmission from the        serving TP and interference from all TPs outside the CoMP set as        well as interference from the other TPs in the CoMP set. Note        that the covariance matrix for the interference from all other        TPs can be estimated by the UE using resource elements        configured for that purpose by the network. Alternatively, the        UE can be configured by the network to estimate the covariance        matrix for the interference from outside the CoMP set using        certain resource elements. Then, the user can be made to        leverage the fact that it has already estimated the unprecoded        downlink channel matrix from each of the other TPs in its CoMP        set. Using these channel estimates the UE can assume a scaled        identity precoder for each of the other TPs and compute the        respective covariance matrices, which then are added together to        the covariance matrix computed for outside the CoMP set. The sum        covariance matrix is then used to compute the fall back SINRs        and fallback CQIs. Note that the scaling factors in the scaled        identity precoders, respectively, can be informed to the UE in a        semi-static manner and can be based on factors such as the        average traffic loads being served by the other TPs (which are        known to the network). A higher scalar corresponds to a higher        traffic load. Similarly, the covariance matrices for the other        TPs can also be computed by the UE assuming the precoder for        each other TP to be a scaled codeword matrix where the codeword        can be uniformly drawn from a codebook subset. The choice of        subset and the scaling factor (associated with each other TP)        can be conveyed to the UE by the network in a semi-static        manner.    -   Per-point CSI-RS resource feedback with muting for each of the        three CSI-RS resources. To save signaling overhead, in the        fallback CSI only fall CQI(s) are reported, where these CQI(s)        are computed using the PMI reported for the serving TP and the        procedure described above. Alternatively, since the rank        reported for the serving TP under muting can be an aggressive        choice for fallback (recall that the fallback also assumes        interference from the other TP) a separate rank indicator can be        allowed for fallback. Specifically the UE can choose any rank R        less than or equal to the one reported for the serving TP under        muting. Then R columns of the PMI reported for the serving TP        (corresponding to the R highest SINRs recovered from the        associated CQI(s) under muting) are obtained. The fall back        CQI(s) are then computed using this column subset.    -   Per-point CSI-RS resource feedback with muting for each of the        three CSI-RS resources. The network can configure in a        semi-static manner, the TP that the UE must assume to be the        serving TP for computing the fallback CQI(s). The remaining TPs        are then treated as the interferers and the procedure described        above is employed. Alternatively, even the subset among the two        other remaining TPs to be treated as interferers can be conveyed        to the UE by the network in a semi-static manner. The TP (if        any) not in the subset is assumed to be silent while computing        these CQI(s). Notice that there are multiple hypotheses under        which the fallback CQI(s) can be computed depending on the        configured fallback choice of serving and interfering TPs. In        one feedback embodiment, the fallback CQI(s) corresponding to        multiple such choices can be simultaneously reported.        Alternatively, to save feedback overhead they can be reported in        a time multiplexed manner. In particular, the user can be        configured to follow a sequence of reporting in which each        report in the sequence includes fallback CQI(s) computed        according to a particular choice of serving and interfering TPs.        The sequence configuration can be done by the network in a        semi-static manner.    -   Per-point CSI-RS resource feedback with muting for each of the        three CSI-RS resources. The UE dynamically chooses the serving        TP for computing the fallback CQI(s). The remaining TPs are then        treated as the interferers and the procedure described above is        employed. The choice of serving TP can be configured to be the        one which offers the highest rate as per the CQI(s) computed        under muting. Note that in this case the choice is implicity        conveyed to the network via the CQI(s) computed under muting and        hence need not be explicitly indicated. Moreover, the choice can        vary across subbands based on the per subband CQI(s). However,        to enable simpler fallback operation the UE can be configured to        determine a wideband choice based on the sum rate across all        subbbands so that even in this case the choice is implicitly        conveyed. Alternatively, a separate wideband indicator can be        employed to enable the UE to indicate its choice which allows        the UE to arbitrarily decide its choice albeit on a wideband        basis.    -   Per-point CSI-RS resource feedback with muting for each of the        three CSI-RS resources. A common rank constraint on the three        CSI-RS resource feedbacks is enforced. Optionally, in addition        fallback CSI as per any one of the above listed options can also        be reported. Further optionally aggregate CQI(s) computed using        the three PMIs (determined for per-point CSI-RS resource        feedback with muting) assuming joint transmission from all three        TPs are also reported.    -   Per-point CSI-RS resource feedback with muting for each of the        three CSI-RS resources. A common rank constraint on the three        CSI-RS resource feedbacks is enforced. Aggregate CQI(s) computed        using the serving PMI and one other PMI (both determined for        per-point CSI-RS resource feedback with muting) assuming joint        transmission from the corresponding two TPs, with the remaining        TP being silent, are also reported. The wideband choice of the        other TP is also indicated. Optionally, in addition fallback CSI        as per any one of the above listed options can also be reported.

We now consider some further variations that can be employed in the CoMPfeedback format design for measurement set sizes 2 and 3.

-   -   For both measurement set sizes 2 and 3, one option that has been        discussed is the per-point CSI-RS resource feedback with muting        for each of the CSI-RS resources in the measurement set along        with a separate fallback CSI, wherein a common rank restriction        can be imposed on

TABLE 1 Spectral Efficiency (bps/Hz) of CoMP schemes with (RR = 1) andwithout (RR = 0) fallback rank restriction. Scheduling DPS DPS CS/CBCS/CB scheme (RR = 1) (RR = 0) (RR = 1) (RR = 0) cell average 2.3981(1.70%) 2.3579 2.4461 (0.26%)  2.4397 5% cell-edge 0.0976 (2.20%) 0.09550.0898 (−0.44%) 0.0902 Actual BLER 6.02% 7.08% 5.54% 6.10% Empty RBratio   7%   7%   0%   0%

-   -   all reported feedback. Here, we outline an approach (or        procedure) to impose this common rank restriction. In this        approach, the UE first computes its fallback CSI (now including        PMI/CQI(s) and rank indicator) and then computes the other        per-point CSI-RS resource feedback under the restriction that        the rank of the quantization codebook used in each per-point        CSI-RS resource feedback be identical to that in the fallback        CSI. Thus only one rank indicator needs to be signalled.    -   We remark that by imposing the fallback rank restriction we bias        a CoMP UE (i.e., a user with more than one TP in its measurement        set) to report per-point CSI with a lower rank. This is because        the fallback CSI is computed under the assumption of        interference from all non-serving TPs and hence will choose a        lower rank. Put another way, a CoMP user is likely to be a        cell-edge user under fallback single-point scheduling and hence        will support a lower rank. Clearly, imposing this fallback rank        restriction on all per-point CSI will result in disabling        higher-rank transmission for a CoMP user, which might        potentially lower the rate. However, it also has a key        advantage. Note that under rank restriction for each per-point        CSI, the user essentially first determines the optimal        un-quantized channel approximation of the given rank and then        quantizes it. Then, an important fact is that given a fixed        quantization load (decided by the codebook size) quantization        error is smaller for lower ranks. The net effect of this is that        the first few dominant singular vectors (which represent        preferred directions) along with the corresponding singular        values are more accurately reported by the user at the expense        of not reporting the remaining ones at all. In the case without        rank restriction the user will typically pick a larger set of        singular vectors to quantize. This results in the central        scheduler knowing more directions and associated gains, albeit        more coarsely.    -   We provide the results to highlight the impact of this fallback        rank restriction in Table 1. For brevity we consider two CoMP        schemes and a suitable CoMP scheduling algorithm. From the        results we see that fallback rank restriction results in almost        no degradation which suggests that accurately knowing a fewer        directions from each CoMP user allows the network to better        manage interference thereby offsetting the loss due to disabling        higher rank transmission to those users. Thus, fallback rank        restriction can be a useful feedback reduction strategy under        limited quantization load.    -   Dynamic Feedforward indication of the feedback hypothesis    -   Recall that we have discussed multiple hypotheses under which        the fallback CQI(s) can be computed depending on the configured        fallback choice of serving and interfering TPs, and where        interference from outside CoMP set is always included. In        general we can refer to each hypothesis as a CSI-process which        is associated with one “channel part” which represents the        choice of the serving TP (or equivalently a non-zero power (NZP)        CSI-RS resource in its measurement set using which a channel        estimate can be obtained) and one “interference part”. This        interference part can in turn be associated with a set of REs        (which is a zero-power (ZP) CSI-RS resource referred to as the        interference measurement resource (IMR)). As discussed before        the UE can be simply told to directly measure or estimate the        covariance matrix of the interference¹ on those REs and it is        up-to the controller to configure on those REs the interference        it wants the UE to measure. Alternatively, the UE can be        configured to measure the interference on an IMR (for instance        the interference from outside CoMP set) and also emulate        additional interference from a subset of TPs in its CoMP set        using the channel estimates determined for those TPs from the        corresponding NZP CSI-RS resources, along with scaled identity        precoders as discussed before. We note that to achieve the        maximal CoMP gains, the network must allow different        CSI-processes to be configured for a UE, with different IMRs        and/or different NZP CSI-RS resources for emulation of        respective interferences. Clearly, all the feedback format        designs discussed earlier (excluding the ones including        aggregate CQI(s)) can be instead described in terms of        configuring multiple CSI-processes. For instance, each per-point        CSI-RS resource feedback described previously is simply a        CSI-process in which the IMR is configured for the UE to measure        the outside CoMP set interference and the NZP-CSI-RS resource is        configured to allow the UE to obtain a channel estimate from the        corresponding TP. ¹For brevity we will henceforth drop the term        “covariance matrix” and just use “measure/estimate the        interference”.    -   In order to limit the overhead and complexity a limit can be        placed on the number of distinct CSI-processes that can be        configured for a UE. Also, we can define the notion of a        CSI-pattern that comprises of a set of CSI-processes. A codebook        of such patterns can be defined and disclosed to the UE in a        semi-static manner. Then, the controller can dynamically signal        an index from the codebook to the UE which identifies a pattern.        The UE can then compute CSI as per each CSI-process in that        pattern and feed them back.    -   To reduce the overhead, while defining a pattern one or more of        its CSI-processes can be marked CQI-only, i.e, the UE does not        compute PMI/RI in the CSI computed for these CSI-processes.        Instead, for each such process it will use the PMI of another        process in that pattern which is not marked CQI-only and has the        same “channel part” (i.e., NZP-CSI-RS-resource), to compute the        CQI(s) associated with the marked process. The process whose PMI        is to be used is also fixed separately for each such CQI-only        marked process. Furthermore, some processes can be marked as        those requiring wideband PMI and/or wideband CQI(s) and        consequently, the UE will only compute and report wideband PMI        and/or wideband CQI(s) for such processes. Additionally, a        separate codebook subset restriction can be placed on each        process and/or a separate maximum rank limit can be placed on        each process. Optionally, a common rank restriction can be        imposed on all processes in a pattern. Further specializing this        restriction, a CSI process in the pattern can be marked to        indicate that the UE should first compute CSI (including RI) for        that process and then use the computed RI for all the remaining        processes. All such optimizations can be done semi-statically        while defining a codebook and the codebook and attributes (or        markings) of each process in each pattern in the codebook are        conveyed to the UE semi-statically. Then the index of a pattern        can be conveyed in a dynamic manner and the UE will report CSI        following the indexed pattern and the attributes of its        constituent CSI processes. Notice that the codebook can be        defined on a UE-specific manner. Alternatively, a codebook can        be defined for each possible measurement set so that each UE can        know the codebook based on its configured measurement set.    -   Let us consider a specific example of a codebook of patterns by        considering a UE with a CoMP measurement set formed by TPs 0,        1, 2. Then, we use three NZP-CSI-RS resources denoted by        NZP-CSI-RS0, NZP-CSI-RS1, NZP-CSI-RS2, respectively, for the        “channel parts” associated with TPs 0, 1 and 2, respectively.        The IMR for measuring the interference outside the CoMP        measurement set is denoted by IMR012. Further, let us define        CSI0, CSI1 and CSI2 to be CSI processes in which “channel parts”        are determined from NZP-CSI-RS0, NZP-CSI-RS1 and NZP-CSI-RS2,        respectively, and the interference parts are denoted by I0, I1        and I2, respectively, where I0 is computed by first        measuring/estimating interference directly on IMR012 and then        emulating the interferences from TPs 1 and 2 and adding them.        The emulation of interference from TP 1 (TP2) is done using the        channel estimated from NZP-CSI-RS1 (NZP-CSI-RS2) and a scaled        identity precoder (or an average over a configured precoder        codebook subset). I1 and I2 are similarly computed by directly        estimating interference in IMR012 and emulating and adding        interference using (NZP-CSI-RS0 and NZP-CSI-RS-2) and        (NZP-CSI-RS0 and NZP-CSI-RS-1), respectively. Finally, let us        define CSIij, where i and j lie in {0, 1, 2}, in which the        channel part is determined using NZP-CSI-RSi and the        interference is computed by measuring/estimating interference        directly on IMR012 and then emulating and adding the        interference from TP in the set {0, 1, 2}\{i, j} using        corresponding NZP-CSI-RS resource. Then a codebook can be        defined as the one including a pattern containing        (CSI0,CSI1,CSI01,CSI10) and another pattern comprising of        (CSI0,CSI2,CSI02,CSI20). Dynamically, the controller can signal        an index corresponding to any one of these two patterns to the        UE. Furthermore, as an option to reduce feedback overhead, in        the pattern (CSI0,CSI1,CSI01,CSI10) CSI01 and CSI10 can be        marked CQI-only and where the CQIs must be computed using the        PMIs determined for CSI0 and CSI1, respectively. Similarly, in        the pattern (CSI0,CSI2,CSI02,CSI20) CSI02 and CSI20 can be        marked CQI-only and where the CQIs must be computed using the        PMIs determined for CSI0 and CSI2, respectively.    -   In another example the codebook can be defined as before with        the following exceptions. In the pattern        (CSI0,CSI2,CSI02,CSI20), the CSI for the process CSI02 is        computed using the the channel part determined as before using        NZP-CSI-RS0 but the interference is directly measured on IMR02        which signifies that in the REs indicated to the UE via this IMR        the controller will ensure that the TPs 0 and 2 will remain        silent so that the UE can directly measure/estimate interference        from outside its CoMP set and the TP 1. Similarly, the CSI for        the process CSI20 is computed using the channel part determined        using NZP-CSI-RS2 and the interference is directly measured on        IMR02. On the other hand, the CSI for the process CSI0 is        computed using the channel part determined using NZP-CSI-RS0 and        the interference directly measured on IMR02 plus the        interference emulated using NZP-CSI-RS2, whereas the CSI for the        process CSI2 is computed using the channel part determined using        NZP-CSI-RS2 and the interference directly measured on IMR02 plus        the interference emulated using NZP-CSI-RS0. The CSI computation        procedure that the UE must follow for pattern        (CSI0,CSI1,CSI01,CSI10) can be similarly specified using IMR01        which signifies that in the REs indicated to the UE via this IMR        the controller will ensure that the TPs 0 and 1 will remain        silent so that the UE can directly measure/estimate interference        from outside its CoMP set and the TP 2. Note that in the second        codebook we need one extra IMR but the UE needs to emulate fewer        interferences compared to the first codebook.    -   Thus by appropriately defining patterns and their CSI        computation procedures, the controller can control the overhead        (in terms of reserving REs for IMRs on a UE specific manner) and        the complexity of interference emulation at the UE. We note that        the complexity of interference emulation at the UE need not be        significantly higher than that of direct measurement/estimation.        Note that in emulation, the UE calculates interference        covariance matrix using estimated channel and pre-computed        “representative” precoder (for example isotropic or an average        across a precoder codebook subset). Even direct measurement of        interference requires implementing covariance estimation        algorithm so there need not be a large complexity saving.        Further, the direct measurement in-fact measures interference        resulting from a particular choice of precoders being employed        by the interfering TPs during the time of measurement. The        interference caused to the UE in the aftermath of scheduling        will most likely result from a different choice of precoders.        While the controller may do some compensation to account for        this mismatch it is complicated by the fact that it does not        know the algorithm adopted by the UE to do the direct        measurement. Considering this the emulation method seems less        biased since it assumes a random or average precoder.

3 PDSCH Mapping in CoMP 3.1 Problems of PDSCH Mapping in CoMP 3.1.1CRS-PDSCH Collision Issues

In order to support legacy (Release 8) UEs, the CRS has to be sent outperiodically [3]. The 3GPP LTE cellular system supports CRS for up to 4antenna ports. The CRS is positioned on the REs with a cell-specificfrequency shift. Thus, if the CRS is transmitted on a subframe, thecell-specific frequency shift and the number of CRS ports specify allthe CRS RE positions on this subframe. Therefore, for the cells or theTPs with different cell IDs, the CRS RE positions are different. Thiswill cause the collision with data symbols transmitted on the PDSCH forthe CoMP transmissions An example of 2 CoMP TPs is shown in FIG. 3. Forthe CoMP JT, the data have to be transmitted through both TPs. Then itis question according to which TP the PDSCH mapping should be configuredby the network and assumed by the UE. On the other hand, for DPS, sinceCoMP transmission is transparent to the UE, the UE does not know whichTP is eventually selected to serve him. Therefore, the UE does not havethe knowledge of the exact CRS RE positions sent from this TP. Again,for DPS, although the UE may still assume the CRS positions based on theserving TPs where the UE receives the control signalling, the mismatchbetween the data symbol and CRS signal will cause the performancedegradation. This seems more severe than the problem in JT as all thedata symbols on the collided REs are missed for detection. There is nosuch collision issue for the CoMP CS/CB transmission scheme since inCS/CB as the transmission is always performed from the serving TP.

Such collision problem is also arise for the CoMP TPs with the same cellID. When the number of antenna ports is the same among all the TPs withthe same cell ID, there is no issue since the CRS positions are exactlythe same for all the TPs. However, in some cases, e.g., the HetNet, thenumber of antenna ports may be different among the coordinated TPs. Thelow power nodes might be equipped with less antennas than the macro basestation. For the CoMP TPs with the same cell ID but different number ofantenna ports, i.e., asymmetric antenna settings, the CRS for the TPwith more antenna ports will collide with the PDSCH for the TP with lessantenna ports. An example is shown in FIG. 4, where the TP on the righthas 4 antenna ports and the left has 2 antenna ports. We can see thatthe TP with 4 antenna ports has 4 CRS REs collided with the TP with 2antenna ports on the data REs. Please note that the asymmetric antennasetting also exists for the CoMP TPs with different cell IDs. Since thecoded QAM modulated symbol sequence is sequentially mapped to the PDSCHRE resources, if the number of CRS REs are different, the UE will not beable to decode the sequence at all due to the shifting of QAM symbolsequence. This is more severe than the CRS interference. If the numberof CRS ports is fixed to be the same for different TPs in the clusterwith the same cell ID even when the number of physical antennas forthose TPs is different, then there is no collision issue. However, theCRS based channel estimation will have some performance degradation.

In the DL transmission there are some subframes which are configured asMBSFN subframes². The CRS is not transmitted on those MBSFN subframes.Hence, CRS-PDSCH collision will also occur when the CoMP TPs do not havethe same MBSFN subframe configurations. For example, at a time instance,one TP is on the non-MBSFN subframe with CRS transmitted on some REs,while at the same time, another TP in the measurement set is on theMBSFN subframe. The PDSCH mapping is then different for these two TPs onthis subframe. Then if CoMP JT or DPS is realized among these two TPs,CRS-PDSCH collision occurs. ²MBSFN stands for Multicast/Broadcast over aSingle Frequency Network

3.1.2 PDSCH Starting Point

In a subframe, the first several OFDM symbols are allocated for sendingcontrol signaling, i.e., PDCCH, in LTE and LTE-A systems. The datachannel PDSCH starts from the next OFDM symbol after PDCCH. Fordifferent transmission points, the numbers of OFDM symbols for PDCCHtransmission can be different. Consequently, the starting points forPDSCH may be different. Again, since the coded QAM sequence issequentially mapped to the PDSCH RE resources, the mismatch of PDSCHstarting points among TPs in the CoMP set will cause the issue for bothjoint transmission and DPS in CoMP transmissions if UE does not know thestart point of PDSCH. An example is shown in FIG. 5.

3.2 PDSCH Mapping in CoMP

We can see due to the aforementioned issues of PDSCH RE mapping in CoMP,some assumptions have to be made or some signaling is needed to solvethe problems in order to make CoMP work properly in LTE-A systems. Wenow consider the following alternatives on the PDSCH mapping in CoMP.

3.2.1 Alignment with the Serving Cell

All the information and signalling of the serving cell are known to theUE. Thus, a simple solution without additional signaling is described asfollows

-   -   The CoMP UE assumes that the PDSCH mapping is always aligned        with that in the serving cell including the PDSCH starting point        and the CRS RE positions. The network follows this assumption to        perform PDSCH mapping for CoMP transmissions. No additional        control signal is needed as the UE always assumes such PDSCH        mapping in the single-cell non-CoMP transmissions. However, this        mutual assumption needs to be specified so that the network will        follow this principle for the PDSCH mapping to allocate QAM data        symbols when CoMP JT or DPS transmissions are scheduled, which        is different from the single-cell non-CoMP transmissions.

For CoMP JT, if the PDCCH region (number of OFDM symbols for PDCCH) froma co-scheduled CoMP TP (other than the serving cell) is larger than thatin the serving cell, with above PDSCH mapping approach, the PDSCH datasymbols in the PDCCH mismatching region are only transmitted from theserving cell, i.e., non-CoMP transmissions, and will experience theinterference from PDCCH signals from this co-scheduled CoMP TP. If thePDCCH region from a co-scheduled CoMP TP (other than the serving cell)is smaller than that in the serving cell, then no data will betransmitted on the PDSCH REs in the PDCCH mismatching region at theco-scheduled CoMP TP. Those REs can be muted.

For DPS CoMP scheme, if the selected TP for transmission is the servingcell TP, there is no PDCCH (or PDSCH starting point) mismatch. Thusthere is no spectral efficiency loss. If the PDCCH region of theselected TP is larger than that of the serving cell, the PDSCH mappingis still configured as that of the serving cell, but with the QAMsymbols in the PDCCH mismatching region being punctured. Since theselected transmit TP is transparent to the UE and the UE does not havethe knowledge of the QAM symbol being punctured in the PDCCH mismatchingregion, UE receives totally irrelevant PDCCH signals on these REpositions to decode. If the PDCCH region of the selected TP is smallerthan that of the serving cell, since the UE assumes that the PDSCHmapping is aligned with that of the serving cell, the OFDM symbol orsymbols after PDCCH of the selected TP that collides with the PDCCHregion of the serving cell will not be used for data transmission. Thenetwork will configure the PDSCH starting point of the selected transmitTP same as that of the serving TP.

Similarly for the CRS/PDSCH collision case. For CoMP JT, on all CRS REpositions in the transmit TPs other than the serving cell, fully CoMPjoint transmission among all CoMP transmit TPs cannot be achieved. OnlyJT on the TP subset is possible. The data symbols on these RE positionswill experience the interference from the CRS transmissions in other TPsin the CoMP transmission set. For the CRS RE positions of the servingcell, no data will be transmitted at other TPs in the CoMP set as the UEassumes that these RE are the CRS. For CoMP DPS, if the selectedtransmitting TP is different from the serving cell, the network willpuncture (not to transmit) the symbols on the CRS positions of theselected transmit TP and skip the REs that are the CRS RE positions ofthe serving cell for the data symbols.

We can see that this approach incurs no additional signal thus has theminimum standard impact. However the spectral efficiency is low due topossible waste of resources and strong interference in the CRS-PDSCH REcollision region.

3.2.2 Collision Avoidance with Semi-Static Signaling

Several methods to solve the CRS/PDSCH collision issue are summarized in[4]. Among the transparent approaches described in [4], one scheme is totransmit the data for CoMP UEs on the MBSFN subframe in which there isno CRS transmission. This restriction limits the resource utilizationfor CoMP transmissions. The second solution is not to transmit data atall for the CRS OFDM symbols, meaning that the entire OFDM symbolcontaining the CRS for any TP in the CoMP set is excluded for datatransmissions in CoMP systems. Obviously this approach wastes theresources and degrades the spectral efficiency performance for CoMP.Another transparent solution is just to perform the CoMP for the TPswith the same cell ID. However, it has been agreed that CoMPtransmissions can be performed for the cells with different cell IDs.Also as aforementioned, single cell ID CoMP does not solve the collisionproblem for the CoMP TPs with different number of antenna ports. We cansee that all these approaches are not efficient. There are also someother non-transparent approaches, e.g., signaling the UE the CoMPtransmission TP or TPs (for DPS or JT) so that the UE knows the activeTP set and the data can be allocated to the REs without collision.Another non-transparent approach is dynamic or semi-static CRS mappingpattern signalling. Also since the CoMP transmission is dynamicscheduled and UE specific, the signaling of the active CoMP TP set orCRS mapping patterns will significantly increase the DL signalingoverhead.

We now provide some efficient CoMP transparent solutions to address theCRS/PDSCH collision issue. We know that in the CoMP system, the networkconfigures and signals the UE the TP set for which UE measures thechannels. Such TP set is called measurement set. The CoMP transmissionTP or TPs will be selected from the measurement set. First we assumethat the UE knows the number of CRS antenna ports for each TP in themeasurement set and provide the following resource mapping approach.

-   -   The union of the REs allocated for CRS transmissions for the TPs        in the measurement set of a CoMP UE are excluded from the        resource mapping for the CoMP (JT or DPS) data transmissions in        PDSCH for this UE. In other words, the resource mapping on the        PDSCH for a CoMP UE should avoids any RE position that is        allocated for a CRS transmission in any TP in the measurement        set for this UE.

If the CoMP UE already knows the CRS information of TPs in itsmeasurement set, the union of the CRS RE positions are then known to theUE. Thus the resource mapping on an RB is known to both network and theUE for transmission and detection. Also since the measurement set isusually small, the union of the CRS RE positions are less than thenumber of REs on the OFDM symbols containing a CRS for any TP.Therefore, the proposed transparent approach is more efficient than theexisting approaches. Although this resource mapping is user specific,however, it does not increase much complexity on the network side as thenetwork already manages the user specific CoMP transmissionsdynamically. Moreover, this proposed approach can be applied to both thecollision cases with the different cell ID and with the same cell ID butasymmetric antenna settings. The resource mapping solutions for theexamples shown in FIG. 3 and FIG. 4 are illustrated on the left portionand right portion of FIG. 6, respectively. We assume that for eachexample there are only two TPs in the measurement set. We can see thatfrom the left plot of FIG. 6, the union of CRS RE positions in PDSCHfrom two TPs with different cell ID are excluded for data mapping. Onthe right side, the union of the CRS RE positions excluded from the datatransmission are essentially the same CRS REs for the TP with 4 CRSantenna ports. Therefore, for the TPs with the same cell ID, thesolution can be rewritten as follows.

-   -   For the CoMP TPs with the same cell ID, the resource mapping for        either JT or DPS CoMP data transmissions on the PDSCH for the        CoMP UE is according to that of the TP with the maximum number        of CRS antenna ports in the measurement set of this UE.

A variation of the proposed scheme is that the network broadcasts theCRS pattern information, which may include the cell ID or the frequencyshift of the CRS RE position, and the number of CRS antenna ports, ofall TPs in the CoMP cluster, the largest TP set for CoMP network basedon the network deployment.³ For the CoMP cluster with the same cell ID,since the cell ID is known to the UE, only the maximum number of CRSantenna ports is broadcasted to all UEs served by the CoMP cluster. Thenthe resource mapping for all CoMP UE is to avoid the union of the CRS REpositions for all TPs in the CoMP cluster with different cell ID, or theCRS RE positions according to the TP with the maximum number of CRSantenna ports. This approach is not UE specific, thus does not introduceadditional complexity on the resource mapping on the network side.However, this approach may be only suitable for the scenario of the samecell ID CoMP as the excluded RE positions are at most the onescorresponding to the largest possible number, which is 4, of CRS antennaports. For the CoMP cluster with different cell IDs, this approach isnot efficient since the size of the CoMP cluster is usually much largerthan the size of the UE specific CoMP measurement set. With a large sizeof CoMP cluster, this approach might eventually exclude the any OFDMsymbol which contains a CRS RE for some TP. ³CoMP measurement set is aUE specific subset of TPs in the CoMP cluster.

CRS is mainly used for LTE (release 8) UEs for channel estimation anddata symbol detection. In LTE Advanced (release 10 or later) systems, aUE uses CSI-RS to estimate the channel. The UE may not monitor or detectthe CRS. Thus, the UE may not be able to know the frequency shift of CRSposition or the number of CRS antenna ports, consequently the CRS REmapping pattern, for the TPs in its measurement set. For this case, wethen propose the following alternatives.

-   (Alt-CRS-1.1): The network semi-statically signals the UE the CRS    frequency shift for each TP and maximum number of CRS antenna ports    of the TPs in the UE's measurement set. The UE then assumes that the    CRS pattern for each TP follows the CRS positions corresponding to    the maximum number of CRS antenna ports. The PDSCH mapping at the    base station for the CoMP data transmission thus follows the same    assumption of the union of CRS positions for this CoMP UE or    according to the PDSCH mapping of the serving cell, which is known    to the UE with a semi-statically signalled indicator.-   (Alt-CRS-1.2): The network semi-statically signals the UE the CRS    frequency shift and the number of CRS antenna ports for each TP in    the UE's measurement set. The UE can then obtain the CRS pattern for    each TP in the measurement set. The PDSCH mapping at the base    station for the CoMP data transmission thus follows the same    assumption of the union of CRS positions for this CoMP UE or    according to the PDSCH mapping of the serving cell.-   (Alt-CRS-1.3): The network semi-statically signals the UE the cell    ID and the number of CRS antenna ports for each in the measurement    set. The UE can then obtain the CRS pattern for each TP in the    measurement set. The PDSCH mapping at the base station for the CoMP    data transmission thus follows the same assumption of the union of    CRS positions for this CoMP UE or according to the PDSCH mapping of    the serving cell.

With the knowledge of CRS frequency shift and number of CRS antennaports, the UE knows the CRS pattern or RE positions. Also the CRS REpositions for less antenna ports are the subset of that for more antennaports. Knowing the cell ID and the CRS pattern of each TP in themeasurement set, the UE is able to detect CRS signal and can thenperform interference cancellation to improve the receiver performance ifsome data are transmitted in some PDSCH REs at one TP that are collidedwith the CRS REs on the other TP in the CoMP set. The information ofMBSFN subframes, MBSFN subframe configuration, at each TP in themeasurement set can also be signalled to the CoMP UE semi-statically.For above three alternatives, we may reduce the number of muted CRS REs,consequently increase the spectral efficiency by only excluding theunion of CRS REs of the TPs in the measurements that are on thenon-MBSFN subframe from the PDSCH mapping.

To obtain the union of the CRS RE patterns at the CoMP UE, the networkfirst semi-statically signal the frequency shift, v_(m), and number ofCRS ports, p_(m), m=1, . . . , M for M TPs in the measurement set as inAlt-CRS-1.2 listed above. Denote the set A_(m) ^(RE)(v_(m), p_(m)) asthe set of CRS RE positions of the mth TP in the measurement set. Theunion of all CRS REs in the measurement set is then given by ∪_(m) A_(m)^(RE)(v_(m), p_(m)). In Alt-CRS-1.1, the maximum number of CRS antennaports of the TPs in the measurement set, i.e., p*=max_(m)p_(m) issignalled to the UE. The set of CRS REs for TP-m assumed at the UE isthen A_(m) ^(RE)(v_(m), p*). Note that we have A_(m) ^(RE)(v_(m),p_(m))⊂A_(m) ^(RE)(v_(m),p*). Then for Alt-CRS-1.1, all CRS REs in the∪_(m) A_(m) ^(RE)(v_(m),p*) are excluded from the PDSCH mapping. ForAlt-CRS-1.3, if the cell-ID of the TPs in the CoMP set is signalled tothe UE, the UE is then able to deduce the CRS frequency shift ∪_(m).With the number of CRS ports or maximum number of CRS ports informed tothe UE, the PDSCH mapping in Alt-CRS-1.3 is again to avoid the union ofthe CRS REs, i.e., ∪_(m) A_(m) ^(RE)(v_(m), p_(m)) or ∪_(m) A_(m)^(RE)(v_(m), p*), as in Alt-CRS-1.2 or Alt-CRS-1.1. Denote I_(m)(t)ε{0,1} as the indicator of MBSFN subframe on the tth subframe for the mth TPin the measurement set, i.e., I_(m)(t)=1 indicates that the subframe-tof TP-m is a MBSFN subframe, and I_(m)(t)=0 otherwise. If the MBSFNsubframe configurations are signalled to the CoMP UE, the UE is able toobtain I_(m)(t), ∀m, t. Then the union of the CRS REs on the subframe

TABLE 2 CoMP PDSCH RE mapping indication with only the semi-staticalsignalling (1-bit). CoMP PDSCH mapping indicator CoMP PDSCH RE Mapping 0according to that of the serving cell 1 PDSCH RE mapping on a subframeexcluding the union of the CRS REs of the TPs in the measurement set onthat subframet, ∪_(m|I) _(m) _((t)=0)A_(m) ^(RE) (v_(m), p_(m)) or ∪_(m|I) _(m(t)=0)A_(m) ^(RE) (v_(m), p*), are excluded from the PDSCH RE mapping on thetth subframe in Alt-CRS-1.1, Alt-CRS-1.2, or Alt-CRS-1.3.

To also support the CoMP CS/CB transmissions which the PDSCH mapping isconfigured according to that for the anchor serving cell, we then useone additional bit along with the signals of the CRS RE patterns to theUE to indicate that the PDSCH RE mapping is according to the servingcell or around all CRS positions in the measurement set, as shown inTable 2. Note that the union of the CRS REs is the union of the existingCRS REs in that subframe if MBSFN subframe configurations of the TPs inthe measurement set are known to the UE.

We now discuss the benefit of the above semi-static approaches over thedefault approach which always assumes the PDSCH mapping of the anchorserving cell. In the default approach, eNB configures PDSCH RE mappingfor any transmitting TP as that for the serving cell. In DPS, when a TPother than the serving TP in the measurement set is transmitting, thePDSCH on the CRS positions for this TP will not be used for datatransmission. If the UE assumes the serving cell PDSCH mapping, it wouldstill try to decode the data on these CRS positions which actually donot carry any data information, resulting in receiving some noisesignals, so called dirty data/bits. A simple simulation is thenperformed to evaluate the performance of these scenarios. A length-576information bits are encoded using the LTE turbo code of rate-½. Weassume there are total 5% coded bits affected by CRS/PDSCH collisions.We the compare the performance of this rate-½ code in AWGN channel withpuncturing 5% coded bits (PDSCH muting), 5% dirty received data (purelynoise), and 2.5% puncturing plus 2.5% dirty data. Puncturing or muting5% coded bits represents the above approaches that avoid thetransmission on the collided REs. The case of 2.5% punctured bits plus2.5% dirty data represents the DPS with default PDSCH mapping. The caseof 5% dirty data represents the DPS scenario in which the TP other thanthe serving TP is transmitting on a non-MBSFN subframe, while theserving TP is on its MBSFN subframe. The block error rate (BLER) resultsof these cases are shown in FIG. 9. We can see that with 5% dirty bits,there is significant performance degradation. With a half of dirty bitson the collided RE positions, there is still an observable performanceloss compared to RE muting.

We now consider the data symbol sequence mapping or allocations for theproposed resource mapping with CRS/PDSCH collision avoidance. For anymethod with CRS/PDSCH collision avoidance, the number of REs in an RBfor the CoMP data transmission will be less than that for conventionalsingle-cell or CoMP CS/CB transmissions. Then the assigned transmissionblock size (TBS) should be changed corresponding to the change ofavailable RE for data transmission to maintain the same effective datarate for the same modulation and coding scheme (MCS). However, toaccommodate the change of assigned TBS for the proposed schemes forCRS/PDSCH collision avoidance, we might need to change the entire TBStable in [5] eventually which will have a large impact on thespecification. Therefore, we propose the following approach. The TBSassignment still follows the same TBS table in [5] and obtain the samedata symbol sequence, e.g. S₀, S₁, . . . . We take the case in the FIG.3 as the example. We first allocate the data symbol for the UE accordingto the data transmission on the serving cell or TP as shown in the leftpart of FIG. 7. For the resource mapping with CRS/PDSCH collisionavoidance, as shown in the right part of FIG. 7, the network or CoMPactive TP or TPs simply puncture and do not transmit the originallyallocated data symbols that collides with the CRS RE positions on otherTPs in the CoMP measurement set of this UE. Since the proposed resourcemapping for CRS/PDSCH collision avoidance does not exclude many REs fordata transmission, the slight increase of the final effectiveinformation rate will have nearly no impact on the receiver performance.

The alternative approach is shown on the right side of FIG. 8, in whichthe network sequentially allocates the data symbols to the REs withoutplacing any symbol on the collided RE. Then with this approach, somedata symbols at the end of symbol sequence will not be allocated ortransmitted. Although the final effective information rate is the sameas that in the previous approach, due to sub-block interleaving,puncturing consecutive data symbols at the end of sequence may incurrelatively larger performance degradation.

The PDSCH starting point might also need to be signalled to the UE in asemi-static manner. The following schemes thus take care of the PDSCHstarting point, if this is necessary.

-   -   The network semi-statically informs the UE the union of the CRS        RE positions in the CoMP measurement set of the UE. The network        also semi-statically configures and signals the UE the starting        point of the PDSCH. The network then configures the QAM symbol        to PDSCH RE mapping from the configured semi-static PDSCH        starting point. Then network either follows the serving cell CRS        pattern for the sequential QAM symbol to PDSCH RE mapping or        perform the QAM symbol to PDSCH RE mapping sequentially to avoid        the union of CRS positions in the CoMP measurement set.    -   The network semi-statically informs the UE either the frequency        shift of CRS position or the cell ID, and the number of antenna        ports for each TP in the CoMP measurement set of the UE. The        network also semi-statically configures and signals the UE the        starting point of the PDSCH. The network then configures the QAM        symbol to PDSCH RE mapping according to the semi-statically        configured PDSCH starting point. And the network either follows        the serving cell CRS pattern for the sequential QAM symbol to        PDSCH RE mapping or configures the QAM symbol to PDSCH RE        mapping sequential to avoid the union of CRS positions in the        CoMP measurement set.

Note that in above approaches the PDSCH start point is assumed to besignaled to UE separately. We can also consider the followingsemi-static approach with a 2-bit indicator. Semi-statically signallingthe PDSCH start point can then be embedded to this approach withoutincreasing the number of bits for the CoMP PDSCH mapping indicator.

-   -   The network semi-statically informs the UE either the frequency        shift of CRS position or the cell ID, and the number of CRS        ports for each TP in the CoMP measurement set of the UE. The        network also semi-statically configures and signals the UE the        starting point of PDSCH and which CRS pattern for the PDSCH        mapping. The network then configures the QAM symbol to PDSCH RE        mapping according to the PDSCH mapping of one TP or the PDSCH        mapping by excluding the union of CRS RE position of the TPs in        the measurement set on that subframe, which is informed to the        UE with a semi-statically signaled indictor from the network.        The network also configures the PDSCH mapping according to the        semi-statically configured PDSCH starting point if it is        necessary, which is known to the UE with the same indicator.

This can be implemented by tagging the CRS information and PDSCHstarting point with the TP index. Then the network signals the UE toindicate the index of TP which the network will configure the PDSCHmapping according to. Since there are at most 3 TPs in a CoMPmeasurement set in current standard, a two-bit indicator is enough tocarry such information. We can also include the option of the PDSCHmapping around of all the CRS REs in a subframe as shown in Table 3.This approach is particularly useful when the cell range expansion isapplied to some UEs in the HetNet scenario, in which the network mayalways configure the macro cell eNB for the DL data transmission. Asaforementioned, the indicator in above table can be applied to PDSCH REmapping to avoid the CRS/PDSCH collision only, or also including thePDSCH starting point. For the case of indicator being 11, the PDSCHstarting point can be the largest or the smallest number of the PDSCHstarting points among that of the TPs in the measurement set.

TABLE 3 CoMP PDSCH RE mapping indication with semi-statical signalingonly (2-bit). CoMP PDSCH mapping indicator CoMP PDSCH RE Mapping 00PDSCH RE mapping according that of TP-1 in the measurement set (assumingit is serving cell without loss of generality) 01 PDSCH RE mappingaccording that of the TP-2 in the measurement set 10 PDSCH RE mappingaccording that of the TP-3 in the measurement set 11 PDSCH RE mapping ona subframe excluding the union of CRS RE positions of the TPs in themeasurement set on that subframe

3.2.3 Dynamic Signaling of the PDSCH Mapping

Although the network can semi-statically inform the UE the PDSCH startpoint, however for DPS, if there is a mismatch between the PDSCH startpoints for the TPs in the CoMP measurement set, it will cause spectralefficiency loss and reduce the performance gain of CoMP. To improve theCoMP performance, the PDSCH mapping information including the startingpoint and CRS pattern can be dynamically conveyed to the UE. We thenlist the following alternatives to achieve this goal and support allCoMP transmission schemes with a small signal overhead.

-   (Alt-CRS-2.1) The network semi-statically informs the UE either the    frequency shift of the CRS position or the cell ID, and the number    of CRS antenna ports for each TP in the CoMP measurement set of the    UE. Then the network dynamically signals the UE the PDSCH starting    point that will be configured for the PDSCH mapping. The network    then configures the QAM symbol to PDSCH RE mapping from the    configured PDSCH starting point. And the network either follows the    serving cell CRS pattern for the sequential QAM symbol to PDSCH RE    mapping or configures the QAM symbol to PDSCH RE mapping sequential    to avoid the union of CRS positions in the CoMP measurement set.-   (Alt-CRS-2.2) The network semi-statically informs the UE either the    frequency shift of CRS position or the cell ID, and the number of    CRS antenna ports for each TP in the CoMP measurement set of the UE.    The network also semi-statically signals the UE which TP or which    CRS pattern for the PDSCH mapping. Then the network dynamically    signals the UE the PDSCH starting point that will be configured for    the PDSCH mapping. The network then configures the QAM symbol to    PDSCH RE mapping starting from the dynamically configured PDSCH    starting point and the sequential PDSCH mapping according to the    semi-statical configured CRS pattern or TP for PDSCH mapping.-   (Alt-CRS-2.3) The network semi-statically informs the UE either the    frequency shift of CRS position or the cell ID, and the number of    CRS antenna ports for each TP in the CoMP measurement set of the UE.    Then the network dynamically signals the UE the PDSCH starting point    that will be configured for the PDSCH mapping and which TP or which    CRS pattern for the PDSCH mapping. The CRS pattern for the PDSCH can    be dynamically conveyed to the UE with the indices of the TPs or the    CRS patterns in the CoMP measurement set that have been    semi-statically signaled to the UE. The network then configures the    QAM symbol to PDSCH RE mapping starting from the dynamically    configured PDSCH starting point and the sequential PDSCH mapping    according to the dynamic configured CRS pattern or TP for PDSCH    mapping.

We can see the approach Alt-CRS-2.1 is a simply extension of theprevious semi-static approach with the 1-bit indicator dynamically sentto UE. In the approach Alt-CRS-2.2, the PDSCH RE mapping around the CRSis still following the semi-static approach, but the PDSCH startingpoint is dynamically signaled to the UE. The approach Alt-CRS-2.3 is theextension of the semi-static approach with the 2-bit indicator in Table3 becoming dynamically signaled to the UE. However, with dynamicalsignaling, in Alt-CRS-2.3, it is not efficient to configure the samePDSCH mapping when the indicator is 11 as that in Table 3 for thesemi-static approach. With first three indicator values in Table 3,i.e., the indicator being 00, 01, 10, the PDSCH mapping issues for DPSis already handled. Only the mapping issues for CoMP JT are left, wheremore than one TP will be involved in the transmission. For this case, inthe hybrid approach with dynamical signaling available, instead ofmapping avoiding the CRS positions for all TPs in the cell, it is betterto perform the PDSCH RE mapping sequentially occupying all possible REs.Just on the collided CRS REs, only single TP or the subset of TPs (for3TP JT) involve in the transmissions. We then have the followingalternative scheme.

-   (Alt-CRS-2.3A) The network semi-statically informs the UE either the    frequency shift of CRS position or the cell ID, and the number of    CRS antenna ports for each TP in the CoMP measurement set of the UE.    The network then informs the UE dynamically the CRS pattern that the    PDSCH mapping (and the PDSCH starting point if needed) will follow    by conveying the indices corresponding to them or indicating the UE    the PDSCH mapping (1) excluding the intersection of all CRS RE set    of the TPs in the measurement on that subframe or (2) simply

TABLE 4 CoMP PDSCH RE mapping indication with dynamic indicatorsignaling (2-bit approach). CoMP PDSCH mapping indicator CoMP PDSCH REMapping 00 PDSCH RE mapping according that of the serving cell (assumeTP-1 in the measurement set) 01 PDSCH RE mapping according that of theTP-2 in the measurement set 10 PDSCH RE mapping according that of theTP-3 in the measurement set 11 PDSCH RE mapping by (1) excluding theintersection of all CRS RE set of the TPs in the measurement on thatsubframe or (2) simply occupying all of the CRS REs of the TPs in themeasurement on that subframe

-   -   occupying all of the CRS REs of the TPs in the measurement on        that subframe.

Note that (1) and (2) described in Alt-CRS-2.3A are two options of thisapproach. The dynamic indicator for Alt-CRS-2.3A is then given in Table4. Mathematically, in Alt-CRS-2.3A, when the indicator being 11, thesets of CRS REs A=∪_(m)A_(m) ^(RE)(v_(m), p_(m)) (or A=∪_(m|I) _(m)_((t)=0)A_(m) ^(RE)(v_(m), p_(m))) is excluded from PDSCH mapping orA=.

Since the effective code rate of Alt-CRS-2.3A will be lower than thePDSCH mapping which avoids the union of CRS positions for the TPs in thejoint transmission, there will be a performance gain even with thestrong interference. To illustrate this, we use the previous simpleexample to compare the performances of PDSCH mapping avoiding the CRS inCoMP JT (puncturing/muting) or occupying the CRS REs with transmittingon single TP or subset of CoMP TPs (experiencing stronger noise) usingthe case of rate-½ LTE turbo code in AWGN channel as previouslydescribed. The results are shown in FIG. 10. We can see that even with a6 dB stronger noise, we still observe the performance gain over thepuncturing case, meaning that for CoMP JT it is better to transmit thecoded symbol on the RE positions for some TPs if they are collided withthe CRS REs for other TPs.

If the CRS information of all the CoMP TPs is available at the CoMP UEand CRS interference cancellation can be implemented, the approachAlt-CRS-2.3A certainly provides better performance than the PDSCH REmapping around the CRS RE positions. Or the UE can at least cancel theinterference of the CRS from the serving cell. If the interfering CRS istoo strong, it is then up to UE to decide where to demodulate the CRScollided data symbol or not. When the PDSCH mapping indicator is set tobe 11, the PDSCH starting point can be set with assuming the minimum ormaximum size of PDCCH regions (or PDCCH OFDM symbols) of the TPs in themeasurement set, which are semi-statically informed to the UE.

The foregoing is to be understood as being in every respect illustrativeand exemplary, but not restrictive, and the scope of the inventiondisclosed herein is not to be determined from the Detailed Description,but rather from the claims as interpreted according to the full breadthpermitted by the patent laws. It is to be understood that theembodiments shown and described herein are only illustrative of theprinciples of the present invention and that those skilled in the artmay implement various modifications without departing from the scope andspirit of the invention. Those skilled in the art could implementvarious other feature combinations without departing from the scope andspirit of the invention.

Further System Details A

In this paper we consider Coordinated Multi-Point transmission andreception (CoMP) schemes over heterogenous wireless networks. Theseheterogenous networks comprise of a set of disparate transmission pointsserving multiple users on an available spectrum. To enable betterresource allocation, the set of transmission points is partitioned intoseveral clusters and each cluster is assigned a set of users that itshould serve. Joint resource allocation (scheduling) using alltransmission points in a cluster and a suitable CoMP scheme is possibledue to the availability of fibre backhaul within each cluster. Ourcontributions in this paper are in the design of approximationalgorithms for this joint scheduling problem. We show that the jointscheduling problem is strongly NP-hard and then design an approximationalgorithm that yields a constant factor approximation. To further obtainalgorithms with a substantially reduced complexity, we adopt aniterative framework and design three polynomial time approximationalgorithms, all of which yield constant factor approximations for afixed cluster size. The design of these algorithms also reveals a usefulconnection between the combinatorial auction problem with fractionallysub-additive valuations and the submodular set-function maximizationproblem. We then conduct a thorough evaluation using models andtopologies developed by the 3GPP standards body to emulate suchnetworks. Our evaluations show that by exploiting all the feedbackprovisioned in the standard in a certain manner and by usingwell-designed algorithms, significant CoMP gains can be realized overrealistic heterogenous networks.

1 Introduction

Explosive growth in data traffic is a reality that network operatorsmust provision for. The most potent approach to cater to this explosivegrowth is considered to be cell splitting in which multiple transmissionpoints are placed in a cell traditionally covered by a single macro basestation. Each such transmission point can be a high power macro enhancedbase-station (a.k.a. eNB) but is more likely to be a low-power remoteradio head or a pico base-station of more modest capabilities. Thenetworks formed by such disparate transmission points are referred to asheterogeneous networks (a.k.a. HetNets) and are rightly regarded as thefuture of all next generation wireless networks. In order to keep thenetwork expenditure in check most operators are considering HetNetarchitectures wherein a majority of transmission points (TPs) have verylimited functionalities but rely instead on directions from the eNBs viaa reliable ultra-low latency backhaul. In such a HetNet architecture thebasic coordination unit is referred to as a cluster which consists ofmultiple TPs and can include more than one eNB. Coordinated resourceallocation within a cluster must be accomplished at a very fine timescale, typically once every millisecond. This in turn implies that allTPs within each cluster must have fibre connectivity and hence impactsthe formation of clusters (a.k.a. clustering) which is dictated by theavailable fibre connectivity among transmission points. On the otherhand, coordination among different clusters is expected to be done on amuch slower time-scale since it is assumed that inter-cluster messageexchange can happen only using a much slower backhaul such as an X2interface of about 20 ms round trip delay. Consequently, in such anarchitecture each user can be associated with only one cluster and theassociation of users to clusters depends mainly on user locations, whichin turn depend on their mobilities and hence this association needs tobe done once every few seconds.

In this paper our interest is on the dynamic coordination within eachcluster. Since user association and clustering happen on time scaleswhich are several orders of magnitude coarser, we assume them to begiven and fixed. The design of joint resource allocation within acluster of multiple TPs has been considered in depth in recent years.These techniques range from assuming global knowledge of user channelsstates and their respective data at a central processor, therebyconverting the cluster into one broadcast channel with global knowledge,to one where only user channel states are shared among TPs in a clusterso that each user can be served by only one TP but downlink transmissionparameters (such as beam-vectors and precoders) can still be jointlyoptimized. In addition, distributed methods to realize joint schedulingas well as the impact of imperfections in the transmitter end channelstate information have also been investigated. Our goal in this work isto verify whether the wisdom accrued from all these works aboutsubstantial performance gains being possible if interference is managedvia coordinated resource allocation is valid over real HetNets. Thechallenges over realistic networks are threefold, namely, (i) the needfor low complexity resource allocation algorithms that can beimplemented in very fine time-scales (ii) incomplete/inaccurate channelfeedback from the users and (iii) real propagation environments.Clearly, since no such real HetNets have yet been deployed, we have torely on accurate modeling. Here, to capture the latter two challenges,we rely on the emulation of such networks as specified by the 3GPP LTEstandards body which has considered HetNet deployments in a verycomprehensive manner. In this context, we note that essentially all nextgeneration wireless networks will be based on the LTE standard which isperiodically updated (with each update referred to as a release) tosupport more advanced schemes. Coordinated transmission and reception(CoMP) among multiple TPs in a cluster will be supported starting fromRelease 11 and feedback and feedforward signalling procedures to supportsuch scheduling as well as detailed channel models and networktopologies have been finalized.

The simplest “baseline” approach then to manage dynamic coordinationwithin a cluster is to associate each user with one TP within thecluster from which it receives the strongest average signal power(referred to as its “anchor” TP), and then perform separate single-pointscheduling for each TP with full reuse. While this approach might appearsimplistic and deficient with respect to degree of freedom metrics whichassume a fully connected network, over realistic networks it capturesalmost all of the average spectral efficiency gains promised by cellsplitting. Indeed, after a year long simulation campaign conducted byall leading wireless companies as part of the Release 11standardization, the expectation from more sophisticated jointscheduling schemes in a cluster is mainly to achieve significant gainsin the 5-percentile spectral efficiency while retaining the averagespectral efficiency gains of the baseline, thereby attaining the goal ofimproved user experience by ensuring good data rates irrespective ofuser location. Towards realizing this expectation, we focus on CoMPschemes where each user receives data from at-most one TP on anytime-frequency resource. This restriction is indeed useful sincereceiving data simultaneously from multiple TPs on the same frequencyrequires additional feedback from the users to enable coherentcombining, which unfortunately has not yet been provisioned for. We thenformulate a resource allocation problem which incorporates the mainconstraints and proceed to develop a constant-factor approximationalgorithm based on a novel approach referred to as format balancing. Tomeet the low-complexity benchmark, we adopt an iterative framework anddevelop three approximation algorithms all of which yield constantfactor

TABLE 1 Spectral Efficiency (bps/Hz) of joint versus baselinesingle-point scheduling. Relative gains are over the baseline.Scheduling scheme DPS CS/CB Baseline cell average 1.9187 (−8.01%) 1.9955 (−4.33%)  2.0858 (0%) 5% cell-edge 0.0281 (−36.57%) 0.0292(−34.09%) 0.0443 (0%) cell average* 2.3981 (−1.30%)  2.4461 (0.67%) 2.4297 (0%) 5% cell-edge* 0.0976 (21.09%)  0.0898 (11.41%)  0.0806 (0%)approximations for a fixed cluster size. In the process we discovered auseful connection between the combinatorial auction problem withfractionally sub-additive valuations and the submodular set-functionmaximization problem, which is of independent interest.

Evaluations of our approximation algorithms over simplistic fullyconnected networks with i.i.d. Rayleigh fading and perfect channel stateinformation, proved their superiority over other heuristics anddemonstrated their competitive performance. However, system evaluationsusing the methodology fully conforming to the 3GPP standard revealedquite a different picture. Indeed, this is depicted in Table 1, whereinthe first two columns pertain to joint scheduling and the third oneconsiders the single-point scheduling baseline alluded to earlier. Inthe results given in the first two rows we only exploited the per-userchannel feedback provisioned in the standard and the results werecatastrophic in that joint scheduling yielded much worse results thanthe single-point scheduling baseline. Detailed investigations led toinsights that are captured as observations in the sequel. Eventually, wecould obtain the results in the last two rows of Table 1, where we seethat substantial 5% spectral efficiency gains have been achieved viajoint scheduling. This improvement is also fully compliant with thefeedback provisioned in the standard, as is explained in the sequel.

2 System Model

We consider a downlink heterogenous network with universal frequencyreuse wherein a cluster of B coordinated transmission points (TPs) cansimultaneously transmit on N orthogonal resource blocks (RBs) duringeach scheduling interval. Each TP can be a high power macro base stationor a low power radio remote head and can be equipped with multipletransmit antennas. Each RB is a bandwidth slice and represents theminimum allocation unit. Together, these B TPs serve a pool of K activeusers. We assume a typical HetNet scenario (as defined in the 3GPP LTERel. 11) wherein these B TPs are synchronized and can exchange messagesover a fibre backhaul. Next, the signal received by a user k on RB n canbe written as

$\begin{matrix}{{{y_{k}(n)} = {{\sum\limits_{j = 1}^{B}\; {{H_{k,j}(n)}{x_{j}(n)}}} + {z_{k}(n)}}},} & (1)\end{matrix}$

where H_(k,j)(n) models the MIMO channel between TP j and user k on RB n(which includes small-scale fading, large-scale fading and pathattenuation), while z_(k)(n) is the additive circularly-symmetricGaussian noise vector and x_(j)(n) denotes the signal vector transmittedby TP j on the n^(th) RB.¹ ¹Notice that the model in (1) holds for thecase of orthogonal frequency-division-multiple access (OFDMA) if themaximum signal delay is within the cyclic prefix.

Considering the signal transmitted by a TP, we impose the commonrestriction that each TP is allowed to serve at-most one user on eachRB.² Then, the signal transmitted by TP q on RB n can then be expressedas

x _(q)(n)=W _(q,u)(n)b _(q,u)(n),  (2)

where b_(q,u)(n) is the complex symbol vector transmitted by TP q on RBn intended for some user u using the precoding matrix W_(q,n)(n) whichsatisfies a norm (power) constraint. The number of symbols inb_(q,n)(n), the constellation(s) from which these symbols are drawn andthe underlying outer code as well as the precoding matrix W_(q,n)(n)(whose columns represent directions in a signal space along which thesymbols are sent), all represent parameters which are included in thescheduling decision obtained as the output of a scheduling algorithm.Notice that due to the broadcast nature of the wireless channel, thesignal intended for user u is received as interference by all otherco-scheduled users as well on RB n. This factor significantlycomplicates the scheduling problem since it is no longer meaningful todefine a per-user utility that depends on the resources allocated tothat user alone. ²This restriction is referred to as SU-MIMO per TP andprovides robustness against imperfect and coarse channel feedback fromthe users.

In order to abstract out the details while retaining usefulness, weadopt the notion of a transmission hypothesis. In particular, we definee=(u, f, b) as an element, where u: 1≦u≦K denotes a user, fεF={1, . . ., J} denotes a format drawn from a finite set F of such formats having acardinality J=|F| and b: 1≦b≦B denotes a transmission point (TP). Eachsuch element e=(u, f, b) represents a transmission hypothesis, i.e., thetransmission from TP b using format f intended for user u. Next, we letΩ={e=(u, f, b):1≦u≦K, fεF, 1≦b≦B} denote the ground set of all possiblesuch elements. For any such element we adopt the convention that

e =(u,f,b)

u _(e) =u,f _(e) =f,b _(e) =b,

Then, we let r: 2 ^(Ω) ×N→IR₊ denote the weighted sum rate utilityfunction. For any subset A ⊂ Ω and any RB nεN, r(A, n) yields theweighted sum rate obtained upon transmission using the hypotheses in Aon RB n. The weight associated with each element e (or equivalently useru _(e) ) is an input to the scheduler and is in turn updated using theresulting scheduling decision. In order to disallow the possibility ofthe same TP serving multiple users on the same RB as well as thepossibility of the same user receiving data from multiple TPs on thesame RB, we adopt the convention that

∃ e≠e′εA:u _(e) =u _(e′) or b _(e) =b _(e′)

r( A,n)=0.  (3)

Further, for any A ⊂ Ω we can expand

$\begin{matrix}{{{r( {\underset{\_}{A},n} )} = {\underset{\underset{\_}{e} \in \underset{\_}{A}}{\Sigma}{r_{\underset{\_}{e}}( {\underset{\_}{A},n} )}}},} & (4)\end{matrix}$

where r _(e) (A,n) is the weighted rate obtained for element e orequivalently the user u _(e) and where we set r _(e) (A,n)=0∀eεAwhenever r(A, n)=0. Notice from (1) and (2) that on any RB and for anygiven choice of transmission hypotheses we have a Gaussian interferencechannel formed by the TPs and users contained in those hypotheses.Implicit in this formulation is the assumption that given the choice oftransmission hypotheses on an RB, the aforementioned parameters (such asthe precoders, constellations etc.) are also determined, using which wecan compute the weighted sum rate over the corresponding Gaussianinterference channel. Throughput this paper, we will assume that theweighted sum rate utility function satisfies a natural sub-additivityassumption which says that the rates of elements in a set will notdecrease if some elements are expurgated from that set. In particular,for any subset A ⊂ Ω and any element eεA, defining C=A\e we assume thatfor each nεN

r _(e″)( C,n)≧r _(e″)( A,n),∀ e″εC.  (5)

We consider three different coordinated multi-pointtransmission/reception schemes.

-   -   Coordinated Silencing/Coordinated Beamforming (CS/CB): In this        scheme each scheduled user can be served data only by its        pre-determined “anchor” TP. In other words, the user set {1, . .        . , K} is partitioned into B non-overlapping sets ∪_(j=1)        ^(B)G_(j), where G_(j) is the set of users whose anchor TP is        the j^(th) TP. Consequently, any eεΩ must satisfy u _(e) εG_(b)        _(e) . Interference mitigation can be achieved via proper        selection of overlapping UEs (i.e. UEs co-scheduled on the same        resource block) and their transmission formats. Notice that        silencing, i.e., muting some TPs on an RB is also possible as a        special case.    -   Dynamic Point Selection (DPS): In this scheme a user can be        served by any TP. Interference mitigation can be achieved as in        CS/CB via proper user and format selection. In addition, DPS        allows for an increase in received signal strength by exploiting        short-term fading via per-RB serving TP selection, where by        serving TP we mean the TP that serves data to the user.    -   Constrained Dynamic Point Selection (CDPS): In this constrained        form of DPS, a user can be served by any TP as long as only one        TP serves it on all its assigned RBs. Notice that the        un-constrained DPS allows for more scheduling freedom and offers        the possibility to exploit the frequency selectivity in the        short-term fading. CDPS can potentially reduce the signaling        overhead at the expense of limited scheduling flexibility. Both        DPS and CDPS include CS/CB as a special case.

We now proceed to formulate our resource allocation problem as in (6).

$\begin{matrix}{{\max\limits_{\substack{\{{{\chi_{\underset{\_}{A},n} \in {\{{0,1}\}}},} \\ {{\forall{\underset{\_}{A} \subseteq \underset{\_}{\Omega}}},{n \in N}}\}}}{\underset{\underset{\_}{A} \subseteq \underset{\_}{\Omega}}{\Sigma}\underset{n \in N}{\Sigma}{r( {\underset{\_}{A},n} )}}},{{x_{\underset{\_}{A},n}\underset{\underset{\_}{A} \subseteq \underset{\_}{\Omega}}{\Sigma}\chi_{\underset{\_}{A},n}} \leq 1},{{\forall{{n( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{A},n}} )}( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{B},n}} )}} = 0},{\forall\underset{\_}{A}},{\underset{\_}{B} \subseteq {\underset{\_}{\Omega}\text{:}{\exists{\underset{\_}{e} \in \underset{\_}{A}}}}},{{{{{\underset{\_}{e}}^{\prime} \in \underset{\_}{B}}\&}\mspace{14mu} u_{\underset{\_}{e}}} = u_{{\underset{\_}{e}}^{\prime}}},{{f_{\underset{\_}{e}} \neq f_{{\underset{\_}{e}}^{\prime}}};{{( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{A},n}} )( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{B},n}} )} = 0}},{\forall\underset{\_}{A}},{\underset{\_}{B} \subseteq {\underset{\_}{\Omega}\text{:}{\exists{\underset{\_}{e} \in \underset{\_}{A}}}}},{{{{{\underset{\_}{e}}^{\prime} \in \underset{\_}{B}}\&}\mspace{14mu} u_{\underset{\_}{e}}} = u_{{\underset{\_}{e}}^{\prime}}},{b_{\underset{\_}{e}} \neq b_{{\underset{\_}{e}}^{\prime}}},\lbrack {{for}\mspace{14mu} {CDPS}} \rbrack} & (6)\end{matrix}$

Note that in (6) the first constraint ensures that at-most onetransmission hypotheses is selected on each RB. The second constraintensures that each scheduled user is assigned only one format. The thirdconstraint which is imposed only in the case of CDPS is that a scheduleduser is served by only one TP over all its assigned RBs.

Before proceeding to design approximation algorithms for (6) andderiving their guarantees, we point out the flexibility inherent in theformulation in (6). Each format can for instance be defined as thenumber of symbol streams assigned, in which case the constraint ofat-most one format per scheduled user captures the main constraint inthe LTE standard which is that each scheduled user be assigned the samenumber of streams on all its assigned RBs. In this case, on any RB for agiven transmission hypotheses we have a Gaussian interference channelwhere the number of streams for each transceiver link is now given sothat the rate utility can be evaluated assuming point-to-point Gaussiancodes for each link and any suitable transmit precoding such as SLNRbased, interference alignment based, etc. Alternatively, each format canalso include up-to two QAM constellations in which case we incorporateanother LTE constraint that each scheduled user can be assigned at-mosttwo distinct QAM constellations.³ Our first result is that (6) isunlikely to be optimally solved by a low (polynomial) complexityalgorithm. ³The mapping of each constellation to one or more streams canbe done using the codeword-to-stream mapping defined in LTE.

Theorem 1. The optimization problem in (6) is NP hard. Specifically, forany fixed N≧1 & J≧2, the optimization problem in (6) is strongly NPhard. For any fixed B≧1 & J≧2, the optimization problem in (6) is NPhard.

In Algorithm I, referred to as the format balancing algorithm, we offeran approximation algorithm for (6). This format balancing algorithm isconceptually simple in that the best transmission hypotheses isdetermined separately for each RB. Then, a balancing step is performedon a per-user basis to ensure that each scheduled user is assigned oneformat each. The balancing is done in a “polite” manner in that a useris assigned a format and then scheduled only on RBs where it wasoriginally assigned a higher format. The notion adopted here is that alower format represents a less aggressive choice with respect to theother co-scheduled users. We will show that Algorithm I offers aconstant approximation under the following additional assumption on theutility function that is satisfied by some physically meaningfulutilities.

Assumption 1. For any subset A ⊂ Ω and any element eεA, define anelement e′=(u _(e) ,f,b _(e) ) for any format f≦f _(e) and construct theset B=e′∪A\e. Then, for each nεN we have that

r _(e″)( B,n)≧r _(e″)( A,n),∀ e″εB:e″≠e′

r _(e′)( B,n)≧α_(f,f) _(e) r _(e) ( A,n),  (7)

for some constant α_(f,f) _(e) ε[0,1] where α_(f,f)=1, ∀f. Thisassumption says that upon replacing any one element in A with anotherelement containing the same user and TP but having a smaller (lessaggressive) format, the rate obtained for any other element in A willnot decrease and the rate obtained for the newly inserted element willbe at-least a fraction of the one obtained previously for the replacedelement. Further, specializing this assumption to the case of C=A\e, weget that the sub-additivity condition in (5) is true.

Next, to derive the approximation factor of Algorithm I, we define amatrix MεIR₊ ^(J×J), with M_(i,j) denoting its (i, j)^(th) member, asfollows

$\begin{matrix}{M_{i,j} = \{ \begin{matrix}{\alpha_{i,j},{{{If}\mspace{14mu} i} \leq j}} \\{0\mspace{14mu} {Otherwise}}\end{matrix} } & (8)\end{matrix}$

Notice that since M is upper triangular with unit diagonal elements, itsdeterminant is equal to 1 so that M⁻¹ exists. Then, we let M⁻¹1≧0 denotethe case when M⁻¹ exists and the vector M⁻¹1 is componentwisenon-negative.Theorem 2. The Format Balancing algorithm offers a solution to (6) thathas a worst-case guarantee of at-least Δ when the assumption in (7)holds and where Δ satisfies

$\Delta \geq \frac{1}{J}$

and is obtained as the solution to a linear program,

$\Delta = {\min\limits_{x \in {{IR}_{+}^{J}{m\theta}} \in {IR}_{+}}\{ \theta \}}$s.t.  1^(T)x = S $\begin{matrix}{{{\sum\limits_{j = 1}^{J}\; {M_{i,j}x_{j}}} \leq {\theta \; S}},{\forall i},} & (9)\end{matrix}$

for any arbitrarily fixed constant S>0. In the special case when M⁻¹1≧0,Δ can be obtained in closed form as

$\begin{matrix}{\Delta = {\frac{1}{1^{T}M^{- 1}1}.}} & (10)\end{matrix}$

Proof. Let us analyze the performance of Algorithm I supposing that theassumption in (7) (and hence (5)) holds. Clearly the weighted sum rateΣ_(nεN)r(A ^((n)), n) is an upper bound on the optimal value of (6)since the per-user format constraint is ignored in the former case. Nextconsider format-balancing for a user uε{1, . . . , K} which is presentin an element of at-least one set A ^((n)) for some nεN. Then for such auser u, for each format f let us define

$\begin{matrix}{{{\overset{\sim}{R}( {u,f} )} = {\underset{{n\text{:}{\exists{\underset{\_}{e} \in {{\underset{\_}{A}}^{(n)}\text{:}u_{\underset{\_}{e}}}}}} = {{{u\&}f_{\underset{\_}{e}}} = f}}{\Sigma}{r_{\underset{\_}{e}}( {{\underset{\_}{A}}^{(n)},n} )}}},} & (11)\end{matrix}$

with the understanding that {tilde over (R)}(u, f)=0 if such an elementcannot be found on any RB n. Note then that the weighted rate obtainedfor user u (after step 5 of Algorithm I) is equal to Σ_(f=1) ^(J){tildeover (R)}(u, f) and indeed Σ_(u=1) ^(K)Σ_(f=1) ^(J){tilde over(R)}(u,f)=Σ_(nεN)r(A ^((n)),n). Invoking the second inequality in (7) wecan deduce that for each format f, the weighted rate R(u, f) computed inAlgorithm I satisfies

$\begin{matrix}{{R( {u,f} )} \geq {\underset{{f^{\prime}\text{:}f^{\prime}} \geq f}{\Sigma}\alpha_{f,f^{\prime}}{{\overset{\sim}{R}( {u,f^{\prime}} )}.}}} & (12)\end{matrix}$

Thus upon selecting {circumflex over (f)}=arg max_(f:1≦f≦J)R(u, f) wecan ensure that user u gets a rate at-least

$\begin{matrix}{\max\limits_{{f\text{:}1} \leq f \leq J}{\underset{{f^{\prime}\text{:}f^{\prime}} \geq f}{\Sigma}\alpha_{f,f^{\prime}}{{\overset{\sim}{R}( {u,f^{\prime}} )}.}}} & (13)\end{matrix}$

In addition, since as per {B ^((n))}_(nεN) user u is scheduled only onRBs where it was originally assigned a format no less that {circumflexover (f)}, invoking (7) and (5) we can deduce that on each such RB therates of co-scheduled users are not decreased. Consequently,irrespective of whether the format balancing is done sequentially acrossusers or in parallel for all users, we can conclude that the worst-caseapproximation guarantee of Algorithm I for the given instance isat-least

$\begin{matrix}{{\min\limits_{u}\frac{\max_{{f\text{:}1} \leq f \leq J}{\Sigma_{{f^{\prime}\text{:}f^{\prime}} \geq f}\alpha_{f,f^{\prime}}{\overset{\sim}{R}( {u,f^{\prime}} )}}}{\Sigma_{f = 1}^{J}{\overset{\sim}{R}( {u,f} )}}} = {\min\limits_{u}\frac{\max_{{f\text{:}1} \leq f \leq J}{\Sigma_{f^{\prime} = 1}^{J}M_{f,f^{\prime}}{\overset{\sim}{R}( {u,f^{\prime}} )}}}{\Sigma_{f = 1}^{J}{\overset{\sim}{R}( {u,f} )}}}} & (14)\end{matrix}$

where the outer minimization is over all users who were scheduled onat-least one RB as per the sets {A ^((n))}_(nεN). Thus, the worst-caseapproximation guarantee of Algorithm I over all instances can be lowerbounded using the solution to the problem

$\begin{matrix}{\min\limits_{x \in {IR}_{+}^{J}}\frac{\max_{{f\text{:}1} \leq f \leq J}{\Sigma_{f^{\prime} = 1}^{J}M_{f,f^{\prime}}x_{f^{\prime}}}}{\Sigma_{f = 1}^{J}x_{f}}} & (15)\end{matrix}$

Clearly, since M_(f,f)=1, ∀f we see that the minimal value in (15) canbe no less than

$\frac{1}{J}.$

The remaining parts of the theorem follow upon invoking Proposition 1.Proposition 1. For any matrix MεIR₊ ^(J×J), where J≧1 is a fixedpositive integer, the solution to

$\begin{matrix}{\min\limits_{x \in {IR}_{+}^{J}}\frac{\max_{{i\text{:}1} \leq i \leq J}{\Sigma_{j = 1}^{J}M_{i,j}x_{j}}}{\Sigma_{i = 1}^{J}x_{i}}} & (16)\end{matrix}$

can be found by solving a quasi-convex minimization problem. Moreimportantly, the solution to (16) can also be found by solving thefollowing linear program for any constant S>0,

$\min\limits_{{x \in {IR}_{+}^{J}},{\theta \in {IR}_{+}}}\{ \theta \}$s.t.  1^(T)x = S $\begin{matrix}{{{{\sum\limits_{j = 1}^{J}{M_{i,j}x_{j}}} \leq {\theta \; S}},{\forall{i.}}}\;} & (17)\end{matrix}$

Furthermore, in the special case of M⁻¹1≧0, the solution to (16) can beobtained in closed form as

$\begin{matrix}{{\min\limits_{x \in {IR}_{+}^{J}}\frac{\max_{{i\text{:}1} \leq i \leq J}{\Sigma_{j = 1}^{J}M_{i,j}x_{j}}}{\Sigma_{i = 1}^{J}x_{i}}} = \frac{1}{1^{T}M^{- 1}1}} & (18)\end{matrix}$

Proof. Consider the optimization problem in (16) and suppose {circumflexover (x)} is an optimal solution with max_(i:1≦i≦J)Σ_(j=1)^(J)M_(i,j){circumflex over (x)}_(j)={circumflex over (α)} and1^(T){circumflex over (x)}=Ŝ so that

$\frac{\hat{\alpha}}{\hat{S}}$

is the optimal value for (16). Then, consider the following convexminimization problem for any constant S>0,

$\begin{matrix}{\min\limits_{{x \in {{IR}_{+}^{J}\text{:}1^{T}x}} = S}\{ {\frac{1}{S}{\max\limits_{{i\text{:}1} \leq i \leq J}{\sum\limits_{j = 1}^{J}\; {M_{i,j}x_{j}}}}} \}} & (19)\end{matrix}$

Clearly {tilde over (x)}=γ{circumflex over (x)}, where

${\gamma = \frac{S}{\hat{S}}},$

is feasible for (19) and yields a value

$\frac{\hat{\alpha}}{\hat{S}}.$

This implies that the optimal value of (19) is no greater than

$\frac{\hat{\alpha}}{\hat{S}}.$

However, an optimal value of (19) which is strictly less than

$\frac{\hat{\alpha}}{\hat{S}}$

would result in a contradiction since it would imply that the optimalvalue of (16) is also strictly less than

$\frac{\hat{\alpha}}{\hat{S}}.$

Consequently, for arbitrarily fixed S>0 the optimal value of (19) isidentical to that of (16). Then, (19) can be re-formulated as in (17).Clearly since the constraints and objective in (17) are affine, it is aconvex optimization problem which implies that any solution to the K.K.Tconditions is also globally optimal. Next, the K.K.T conditions for (17)are given by

${{1^{T}x} = S};{x \in {IR}_{+}^{J}};{{\theta \; S} \geq {\sum\limits_{j = 1}^{J}\; {M_{i,j}x_{j}{\forall i}}}}$${{\beta^{T}1} = \frac{1}{S}};{{\beta^{T}M} = {\lambda^{T} + {\delta \; 1^{T}}}};{\beta \in {IR}_{+}^{J}};{\lambda \in {IR}_{+}^{J}}$$\begin{matrix}{{{{\lambda \odot x} = 0};{{\beta \odot ( {{Mx} - {\theta \; S\; 1}} )} = 0};{\delta \in {IR}}},} & (20)\end{matrix}$

where ⊙ denotes the Hadamard product. Next, suppose that M⁻¹1≦0. Then,consider a particular choice

${x = {( {\theta \; S} )M^{- 1}1}};{\theta = \frac{1}{1^{T}M^{- 1}1}}$$\begin{matrix}{{\delta = \frac{1}{S\; 1^{T}M^{- 1}1}};{\lambda = 0};{\beta^{T} = {\delta \; 1^{T}{M^{- 1}.}}}} & (21)\end{matrix}$

It can be verified that the choice in (21) satisfies all the K.K.T.conditions in (20) and hence must yield a global optima for (17) andthus the optimal value for (16). This optimal value can be verified tobe

$\frac{1}{1^{T}M^{- 1}1}.$

We have the following important corollary to Theorem 2. It pertains to aparticular value for matrix M which is obtained when a format i, 1≦i≦Jimplies an assignment of i symbol streams and when the rate function oneach RB for a given hypotheses is computed assuming point-to-pointGaussian codes for each transceiver link, single-user decoding at eachuser and a transmit precoding method from a class of transmit precodingmethods (which includes both SLNR and interference alignment basedprecoding).

Corollary 1. Consider the upper-triangular matrix MεIR₊ ^(J×J), whereJ≧1 is a fixed positive integer, defined as

$\begin{matrix}{M_{i,j} = \{ \begin{matrix}{\frac{i}{j},{{{If}\mspace{14mu} 1} \leq i \leq j \leq J}} \\{0\mspace{14mu} {Otherwise}}\end{matrix} } & (22)\end{matrix}$

Then its inverse is a bi-diagonal matrix given by L=M⁻¹ where

$\begin{matrix}{L_{i,j} = \{ \begin{matrix}{1,{{{If}\mspace{14mu} i} = j}} \\{{- \frac{i}{j}},{{{If}\mspace{14mu} i} = {j - 1}}} \\{0,{Otherwise}}\end{matrix} } & (23)\end{matrix}$

Further, in this ease L1≧0 and we have that

$\begin{matrix}{\Delta = {\frac{1}{\Sigma_{j = 1}^{J}\frac{1}{j}}.}} & (24)\end{matrix}$

Notice from (24) that the approximation factor decays with J as

$\frac{1}{\ln (J)}$

which is much slower than 1/J.

We note that while Algorithm I is conceptually simple and can offer aconstant-factor approximation, its implementation complexity can bequite high. Indeed, its complexity is O(N(KJ)^(B)) and is not feasiblein many scenarios. In this context, we note that since the problem in(6) subsumes the strongly NP hard maximum weight independent set (MWIS)problem, an exponential complexity with respect to B is the likely pricewe have to pay in order to obtain a approximation factor independent ofB. Consequently, henceforth we will adopt an iterative framework todesign approximation algorithms which will make the complexitypolynomial in even B but will introduce a penalty of

$\frac{1}{B}$

in the approximation guarantees.

To design the iterative algorithms, we first define an incremental ratefunction. In particular, for any nεN, any A ⊂ Ω and any eεΩ we define

$\begin{matrix}{{\overset{\sim}{r}( {\underset{\_}{e},\underset{\_}{A},n} )} = ( {{r( {{\underset{\_}{e}\bigcup\underset{\_}{A}},n} )} - {r( {\underset{\_}{A},n} )}} )^{+}} & (25)\end{matrix}$

where (x)⁺=max{0,x}, xεIR. Notice that as a consequence of (3), {tildeover (r)}(e, A, n)=0 if there exists an element e′εA such that b _(e) =b_(e′) or u _(e) =u _(e′). We now define a per-step scheduling problemwhich will be approximately solved in each iteration step. Given a setof elements scheduled on each RB thus far, {A ^((n))}_(n=1) ^(N), alongwith a set of elements B from which new elements can be selected, theper-step scheduling problem is defined as

$\begin{matrix}{{{\max\limits_{\substack{\{{\chi_{\underset{\_}{e},n} \in {{\{{0,1}\}}\text{:}}} \\ {{\underset{\_}{e} \in \underset{\_}{B}},{n \in N}}\}}}{\underset{\underset{\_}{e} \in \underset{\_}{B}}{\Sigma}\underset{n \in N}{\Sigma}{\overset{\sim}{r}( {\underset{\_}{e},{\underset{\_}{A}}^{(n)},n} )}\chi_{\underset{\_}{e},n}\underset{\underset{\_}{e} \in \underset{\_}{B}}{\Sigma}\chi_{\underset{\_}{e},n}}} \leq 1},{{\forall{{n( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{e},n}} )}( {\underset{n \in N}{\Sigma}\chi_{{\underset{\_}{e}}^{\prime},n}} )}} = 0},{\forall\underset{\_}{e}},{{{{\underset{\_}{e}}^{\prime} \subseteq {\underset{\_}{B}\text{:}u_{\underset{\_}{e}}}} = {{u_{{\underset{\_}{e}}^{\prime}}.f_{\underset{\_}{e}}} \neq f_{{\underset{\_}{e}}^{\prime}}}};{{( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{e},n}} )( {\underset{n \in N}{\Sigma}\chi_{{\underset{\_}{e}}^{\prime},n}} )} = 0}},{\forall\underset{\_}{e}},{{{\underset{\_}{e}}^{\prime} \subseteq {\underset{\_}{B}\text{:}u_{\underset{\_}{e}}}} = u_{{\underset{\_}{e}}^{\prime}}},{b_{\underset{\_}{e}} \neq b_{{\underset{\_}{e}}^{\prime}}},\lbrack {{for}\mspace{14mu} {CDPS}} \rbrack} & (26)\end{matrix}$

Next, we define a family of sets I as follows. All singleton elements inΩ are members of I. In addition,

For CS/CB or DPS: AεI If and only if ∀ e,e′εA,u _(e) =u _(e′)

f _(e) =f _(e′)  (27)

For CDPS: AεI If and only if ∀ e,e′εA,u _(e) =u _(e′)

e=e′.  (28)

The family defined above possesses the following property which followsfrom the basic definitions.Proposition 2. The family of sets defined in (27) or (28) is anindependence family. Consequently (Ω,I) is a matroid.

Next, given subsets {A ^((n)) ⊂ Ω}_(nεN) and any S ⊂ Ω, we defineanother set function

$\begin{matrix}{{g( \underset{\_}{S} \middle| \{ {\underset{\_}{A}}^{(n)} \}_{n \in N} )} = {\underset{n \in N}{\Sigma}{\max\limits_{\underset{\_}{e} \in \underset{\_}{S}}\{ {\overset{\sim}{r}( {\underset{\_}{e},{\underset{\_}{A}}^{(n)},n} )} \}}}} & (29)\end{matrix}$

Notice that the set function g(.) collects the best possible incrementalgain on each RB. We are now ready to describe two of our iterativealgorithms. We offer Algorithm II which is a simple iterative algorithm(referred to as the iterative submodular algorithm) to approximatelysolve (6). In addition, when the CoMP scheme is either CS/CB or DPS, wealso provide Algorithm III, referred to as the iterative formatbalancing algorithm, which is another simple approach to approximatelysolve (6). Notice that in each iteration of either iterative algorithm,decisions made in the previous iterations are kept fixed. Newassignments of RBs, serving TPs and formats to users are made by solvingthe “per-step” scheduling problem of (26) and the obtained resultensures an improvement in system utility while maintaining feasibility.The main difference between the two algorithms is in the method used toapproximately solve the per-step scheduling problem. Regarding the nonapplicability of Algorithm III for CDPS, we note that the balancing ineach iteration of Algorithm III is with respect to the format of a user.While such a balancing can also be done with respect to the serving TPof a user, in general no provable guarantees can then be derived sincethe channels seen by a user from any two different TPs in the clustercan be arbitrarily different. Also, the pruning step in eitheralgorithm, given a selected subset S, is done as follows.

$\begin{matrix}{\underset{\_}{B} = \{ \begin{matrix}{{\underset{\_}{B}\backslash \{ {{\underset{\_}{e} \in {\underset{\_}{\Omega}\text{:}{\underset{\_}{e}}^{\prime}} \in \underset{\_}{S}},{u_{\underset{\_}{e}} = {{{u_{{\underset{\_}{e}}^{\prime}}\&}\mspace{14mu} f_{\underset{\_}{e}}} \neq f_{{\underset{\_}{e}}^{\prime}}}}} \}},{{If}\mspace{14mu} {CS}\text{/}{CB}\mspace{14mu} {or}\mspace{14mu} {DPS}}} \\{{\underset{\_}{B}\backslash \{ {{\underset{\_}{e} \in {\underset{\_}{\Omega}\text{:}{\exists{{\underset{\_}{e}}^{\prime} \in \underset{\_}{S}}}}},{u_{\underset{\_}{e}} = {{{u_{{\underset{\_}{e}}^{\prime}}\&}\mspace{14mu} \underset{\_}{e}} \neq {\underset{\_}{e}}^{\prime}}}} \}},{{If}\mspace{14mu} {CDPS}}} \\{{\underset{\_}{B}\backslash \{ {{\underset{\_}{e} \in {\underset{\_}{\Omega}\text{:}{\exists{{\underset{\_}{e}}^{\prime} \in \underset{\_}{S}}}}},{u_{\underset{\_}{e}} = u_{{\underset{\_}{e}}^{\prime}}}} \}},{{If}\mspace{14mu} {aggressive}}}\end{matrix} } & (30)\end{matrix}$

Notice that the aggressive pruning option subsumes the CS/CB or DPSpruning as well as the CDPS one and hence is applicable, if enabled, inall cases. Next, specializing the utility to the single user case wehave the following inequalities:

r( e′,n)≧β_(f) _(e′) _(,f) _(e) r( e,n),∀ e,e′εΩ   (31)

for some constants β_(i,j), 1≦i,j≦J with β_(i,i)=1, ∀i. We then definethe matrix GεIR₊ ^(J×J), where

G _(i,j)=β_(i,j), where β_(i,j)ε[0,1],∀1≦i,j≦J.  (32)

Notice that since we can always set β_(i,j)=0, (31) itself results in noloss of generality. We note that here we allow for the possibility ofβ_(i,j)>0 for i>j so that the matrix G need not be upper triangular.Further, whenever (7) holds we can deduce that β_(i,j)≧α_(i,j)∀1≦i≦j≦J.The following result on the approximation guarantees for these twoalgorithms holds whether or nor aggressive pruning is enabled.Theorem 3. The iterative submodular algorithm offers a solution that hasa worst-case guarantee of at-least

$\frac{1}{2B}.$

For CS/CB or DPS the iterative format balancing algorithm offers asolution that has a worst-case guarantee of at-least

$\frac{\Gamma}{B},$

where Γ satisfies

$\Gamma \geq \frac{1}{J}$

and can be determined via a linear program

$\Gamma = {\min\limits_{{x \in {IR}_{+}^{J}},{\theta \in {IR}_{+}}}\{ \theta \}}$s.t.  1^(T)x = S $\begin{matrix}{{{\sum\limits_{j = 1}^{J}\; {G_{i,j}x_{j}}} \leq {\theta \; S}},{\forall i}} & (33)\end{matrix}$

for any arbitrarily fixed S>0 and with the matrix G being defined in(32). Furthermore, when G⁻¹1

0 we have that

$\Gamma = {\frac{1}{1^{T}G^{- 1}1}.}$

Proof. We first note that since the utility function is sub-additive(i.e., satisfies (5)), for any set A ⊂ Ω and any nεN we have that r(A,n)≦B max _(eεA) r(e, n). Then, given any optimal solution for (6) we canretain the best element (yielding the highest single-user weighted rate)on each RB and the resulting weighted sum rate will be within a fraction

$\frac{1}{B}$

of the optimal one. Moreover, since the solution so obtained is afeasible solution for the per-step scheduling problem in (26) with B=Ωand A ^((n))=φ, ∀n, we can conclude that the optimal solution to theper-step scheduling problem with B=Ω and A ^((n))=φ, ∀n will at-least bewithin

$\frac{1}{B}$

of the one optimal for (6). Also, any feasible solution of (26) isclearly feasible for (6).

Let us now consider the iterative submodular algorithm. Then, note thatthe per-step scheduling problem in (26) can be re-formulated as

$\begin{matrix}{\max\limits_{\underset{\_}{S} \subseteq {\underset{\_}{B}\text{:}\underset{\_}{S}} \in \underset{\_}{\chi}}{g( \underset{\_}{S} \middle| \{ {\underset{\_}{A}}^{(n)} \}_{n \in N} )}} & (34)\end{matrix}$

Notice that since each step of the iterative algorithm yields amonotonic improvement in the utility function along with a solution thatis feasible for (6), it is sufficient to show that the weighted sum rateobtained after the first step is within

$\frac{1}{2}$

its corresponding optimal, i.e., the optimal solution to the per-stepscheduling problem with B=Ω and A ^((n))=φ, ∀n. Towards this end, wenote that the function g: 2 ^(Ω) →IR₊ is a monotonic submodular setfunction and invoking Proposition 2 we see that the problem in (34)(with B=Ω and A ^((n))=φ, ∀n) is that of maximizing a monotonic setfunction over a matroid. It is well known that for this problem a simplegreedy algorithm yields a ½ approximation. Algorithm II is indeed anadaptation of that greedy algorithm to the problem at hand and henceyields a ½ approximation.

Now let us consider the iterative format balancing algorithm and supposethat the selected CoMP scheme is either CS/CB or DPS. Here again we notethat each step of the iterative algorithm yields a monotonic improvementin the utility function along with a solution that is feasible for (6).Consequently, we focus on the first step with B=Ω and A ^((n))=φ, ∀n.Notice that a key difference between the format balancing procedures inAlgorithms I and III is that in the latter case on any RB we allow forthe possibility of assigning a higher format to a user than the onetentatively assigned to that user after the maximization step thatignores the per-user format constraint, as long as the overall weightedsum rate obtained on that RB is improved. Then, using arguments similarto those made to prove Theorem 2 we can show that the solution obtainedyields a weighted sum rate within at-least a fraction Γ of its optimalcounterpart, where Γ is given by (33).

We have the following important corollary to Theorem 3 when specializedto the iterative format balancing algorithm. It pertains to a particularvalue for matrix G which is obtained when a format i, 1≦i≦J implies anassignment of i symbol streams and when the single user rate function oneach RB for a given format is computed assuming point-to-point Gaussiancode, single-user decoding at each user and a precoding method from theaforementioned class of precoding methods (which includes optimalsingle-user precoding when restricted to the single-user case).

Corollary 2. Consider the matrix GεIR₊ ^(J×J), where J≧1 is a fixedpositive integer, defined as

$\begin{matrix}{{G_{i,j} = \frac{\min \{ {i,j} \}}{\max \{ {i,j} \}}},{1 \leq i},{j \leq {J.}}} & (35)\end{matrix}$

Its inverse is a tri-diagonal matrix given by L=G⁻¹ where

$\begin{matrix}{L_{i,j} = \{ \begin{matrix}{{- \frac{j( {j - 1} )}{{2j} - 1}},{{{If}\mspace{14mu} i} = {j - 1}}} \\{\frac{4j^{3}}{{4j^{2}} - 1},{{{If}\mspace{14mu} i} = j}} \\{{- \frac{j( {j + 1} )}{{2j} + 1}},{{{If}\mspace{14mu} i} = j}} \\{0,{Otherwise}}\end{matrix} } & (36)\end{matrix}$

Further, in this case L1

0 and we have that

$\begin{matrix}{\Gamma = {\frac{1}{\Sigma_{j = 1}^{J}\frac{1}{{2( {j - 1} )} + 1}}.}} & (37)\end{matrix}$

Notice from (37) that the approximation factor decays with J as

$\frac{2}{\ln (J)}.$

Also, using (37) we can deduce that for all J≦7 we have Γ>½ so that inthis regime the iterative format balancing algorithm offers a superiorguarantee than the iterative submodular algorithm.

2.1 Implementation Issues

We now briefly discuss some features that can be used to speed up therun time and/or improve the performance of Algorithms II and III.

-   -   Aggressive Pruning: The aggressive pruning option is the most        aggressive option in terms of pruning the pool of elements (that        can be chosen) after each iteration and hence achieves        complexity reduction. Indeed, under this option all elements        containing a user that has been selected before are removed. In        our simulations we observed that while this option causes        negligible degradation in the performance of CS/CB, both DPS and        CDPS actually benefit from this option since it tends to avoid        highly sub-optimal local maxima.    -   Lazy Evaluations: Recall that in each iteration of Algorithm II        we employ a greedy method to approximately maximize a submodular        function. Then the technique of lazy evaluations which exploits        the decreasing marginal gains property of submodular set        functions, can be used to achieve speed up.    -   Suboptimal evaluation of incremental rate function: Here we note        that proper evaluation of the incremental rate function would        require recomputing the parameters such as transmit precoders        even for the users selected in the previous iterations on an RB.        Instead, a sub-optimal evaluation can be done in the        intermediate iterations wherein these parameters associated with        previous decisions are not changed.    -   Post processing: Upon termination of Algorithms II and III, each        scheduled user is assigned a format, a set of RBs and a serving        TP on each such RB. Then, by retaining the format (and the        serving TP in case of CDPS) assigned to each scheduled user and        by assigning the most robust format f=1 to the ones not        scheduled and allowing such users to be served only by their        anchor TPs, we can refine the hypotheses selected on each RB.        Since each user is now assigned one format (and one serving TP        in case of CDPS), the refinement can be done independently        across RBs without violating the at-most one format per        scheduled user constraint (and the at-most one serving TP        constraint in case of CDPS). Any simple refinement rule can be        used as long as it ensures monotonic improvement. In our        simulations we employed sub-optimal incremental rate evaluation        in the intermediate iterations along with a simple greedy        refinement in the post-processing step. We observed that the        benefit from such refinement is largest when the selected CoMP        schemes are either DPS or CDPS.

3 Finite Buffers: Combinatorial Auction

We now incorporate finite buffers into our optimization problem. We willassume that either CS/CB or CDPS is used as the CoMP scheme. Thisassumption is made for convenience in exposition and we note that allthe following results also hold for DPS. Then, letting Q_(u),θ_(u)denote the buffer size (in bits) of user u and its scheduling weight⁴,respectively, we obtain the optimization problem given by ⁴Without lossof optimality, we can assume that the user weights are normalized to liein [0,1].

$\begin{matrix}{{{\max\limits_{\substack{\{{\chi_{\underset{\_}{A},n} \in {{\{{0,1}\}}\text{:}}} \\ {{\underset{\_}{A} \subseteq \underset{\_}{\Omega}},{n \in N}}\}}}{\underset{{u\text{:}u} \in {\{{1,\cdots,K}\}}}{\Sigma}\min \{ {{\underset{{\underset{\_}{e} \in {\underset{\_}{\Omega}\text{:}u_{\underset{\_}{e}}}} = u}{\Sigma}\underset{\underset{\_}{A} \subseteq {\underset{\_}{\Omega}\text{:}\underset{\_}{e}} \in \underset{\_}{A}}{\Sigma}\underset{n \in N}{\Sigma}{r_{\underset{\_}{e}}( {\underset{\_}{A},n} )}\chi_{\underset{\_}{A},n}},{\nu_{u}Q_{u}}} \} \underset{\underset{\_}{A} \subseteq \underset{\_}{\Omega}}{\Sigma}\chi_{\underset{\_}{A},n}}} \leq 1},{{\forall{{n( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{A},n}} )}( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{B},n}} )}} = 0},{\forall\underset{\_}{A}},{\underset{\_}{B} \subseteq {\underset{\_}{\Omega}\text{:}{\exists{\underset{\_}{e} \in \underset{\_}{A}}}}},{{{{{\underset{\_}{e}}^{\prime} \in \underset{\_}{B}}\&}\mspace{14mu} u_{\underset{\_}{e}}} = u_{{\underset{\_}{e}}^{\prime}}},{{f_{\underset{\_}{e}} \neq f_{{\underset{\_}{e}}^{\prime}}};{{( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{A},n}} )( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{B},n}} )} = 0}},{\forall\underset{\_}{A}},{\underset{\_}{B} \subseteq {\underset{\_}{\Omega}\text{:}{\exists{\underset{\_}{e} \in \underset{\_}{A}}}}},{{{{{\underset{\_}{e}}^{\prime} \in \underset{\_}{B}}\&}\mspace{14mu} u_{\underset{\_}{e}}} = u_{{\underset{\_}{e}}^{\prime}}},{b_{\underset{\_}{e}} \neq b_{{\underset{\_}{e}}^{\prime}}},{{for}\mspace{14mu} {CDPS}}} & (38)\end{matrix}$

In order to approximately solve (38) we introduce another simplerproblem given by

$\begin{matrix}{{{\max\limits_{\substack{\{{\chi_{\underset{\_}{e},n} \in {{\{{0,1}\}}\text{:}}} \\ {{\underset{\_}{e} \subseteq \underset{\_}{\Omega}},{n \in N}}\}}}{\underset{{u\text{:}u} \in {\{{1,\cdots,K}\}}}{\Sigma}\min \{ {{\underset{{\underset{\_}{e} \in {\underset{\_}{\Omega}\text{:}u_{\underset{\_}{e}}}} = u}{\Sigma}\underset{n \in N}{\Sigma}{r( {\underset{\_}{e},n} )}\chi_{\underset{\_}{e},n}},{\nu_{u}Q_{u}}} \} \underset{\underset{\_}{e} \subseteq \underset{\_}{\Omega}}{\Sigma}\chi_{\underset{\_}{e},n}}} \leq 1},{{\forall{{n( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{e},n}} )}( {\underset{n \in N}{\Sigma}\chi_{{\underset{\_}{e}}^{\prime},n}} )}} = 0},{\forall\underset{\_}{e}},{{{\underset{\_}{e}}^{\prime} \subseteq {\underset{\_}{\Omega}\text{:}u_{\underset{\_}{e}}}} = u_{{\underset{\_}{e}}^{\prime}}},{{f_{\underset{\_}{e}} \neq f_{{\underset{\_}{e}}^{\prime}}};{{( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{e},n}} )( {\underset{n \in N}{\Sigma}\chi_{{\underset{\_}{e}}^{\prime},n}} )} = 0}},{\forall\underset{\_}{e}},{{{\underset{\_}{e}}^{\prime} \subseteq {\underset{\_}{\Omega}\text{:}u_{\underset{\_}{e}}}} = u_{{\underset{\_}{e}}^{\prime}}},{b_{\underset{\_}{e}} \neq b_{{\underset{\_}{e}}^{\prime}}},{{for}\mspace{14mu} {CDPS}}} & (39)\end{matrix}$

The relation between the optimal solutions to (38) and (39) is given bythe following result.

Proposition 3. The optimal solution to (39) is feasible for (38) andyields a value that is no less than a factor

$\frac{1}{B}$

times that yielded by the optimal solution to (38).Proof. Consider then an optimal allocation to (38), say {Â^((n))}_(nεN), and for that solution let G_(b)′ denote the set of usersserved by TP b where b=1, . . . , B. Under both CS/CB and CDPS we havethat these sets are non overlapping, i.e., G_(k)′∪G_(j)′=φ, ∀k≠j.Further, the overall utility can be expanded as Σ_(b=1) ^(B)R_(b), whereR_(b) is the weighted sum of rates of all users in G_(b)′, wherein theper-user finite buffer constraints are included. Next, consider a TP band suppose that on each RB nεN a genie removes the interference causedto the user being served by TP b from co-scheduled transmissions byother TPs. Invoking the property in (5), we can see the resultingweighted sum rate {circumflex over (R)}_(b) will be at-least as large asR_(b). However, {circumflex over (R)}_(b) can be achieved by aparticular solution to (39) derived from {Â ^((n))}_(nεN), wherein onlythe element containing a user in is retained in each Â ^((n)) (noticethat there can only be one such element in each Â ^((n))) and the othersare expurgated. This implies that the optimal solution to (39) yields avalue that is an upper-bound to each {circumflex over (R)}_(b), b=1, . .. , B, which in turn allows us to conclude that the theorem is true.

We now offer the following proposition. We will use per-user utility andvaluations interchangeably.

Proposition 4. The problem in (39) is a combinatorial auction problemwith fractionally sub-additive valuations.Proof. We introduce a utility function h:{1, . . . , K}×2^(N)→IR₊defined with some abuse of notation as

$\begin{matrix}{{h( {u,R} )} = \{ \begin{matrix}{{\min \{ {{\nu_{u}Q_{u}},{\max_{f \in F}{\Sigma_{n \in R}{r( {( {u,f,b} ),n} )}}}} \}},{{{CS}\text{/}{CB}\mspace{14mu} b\text{:}u} \in G_{b}}} \\{{\min \{ {{\nu_{u}Q_{u}},{\max_{{f \in F},{b \in {\{{1,\cdots,B}\}}}}{\Sigma_{n \in R}{r( {( {u,f,b} ),n} )}}}} \}},{CDPS}}\end{matrix} } & (40)\end{matrix}$

Then, we can re-formulate the problem in (39) as

$\begin{matrix}{{\max\limits_{\underset{{{u \in {\{{1,\ldots \mspace{14mu},K}\}}},{R \subseteq N}}\}}{{\{{{\overset{\sim}{\chi}}_{u,R} \in {\{{0,1}\}}}\}}:}}{\sum\limits_{u \in {\{{1,\ldots \mspace{14mu},K}\}}}{\sum\limits_{R \subseteq N}{{h( {u,R} )}{\overset{\sim}{\chi}}_{u,R}}}}}{{{\sum\limits_{R:{n \in R}}{\sum\limits_{u}{\overset{\sim}{\chi}}_{u,R}}} \leq 1},{\forall{n \in N}}}{{{\sum\limits_{R}{\overset{\sim}{\chi}}_{u,R}} \leq 1},{\forall{u \in {\{ {1,\ldots \mspace{14mu},K} \}.}}}}} & (41)\end{matrix}$

Clearly the problem in (41) is in the form of a standard combinatorialauction problem (a.k.a. welfare maximization problem) where objects in Nhave to assigned in an non-overlapping manner to the K users. Then, itremains to be shown that for each user u, the set function h(u, :) isfractionally sub-additive. Invoking the definition of such a function,we have to prove that the following property holds. For any given setS⊂N and any fractional cover {η_(q),T_(q)} of S, i.e., η_(q)ε[0,1],T_(q) ⊂N∀q and Σ_(q:nεT) _(q) η_(q)≧1, ∀nεS, we have to prove that

$\begin{matrix}{{h( {u,S} )} \leq {\sum\limits_{q}{\eta_{q}{{h( {u,T_{q}} )}.}}}} & (42)\end{matrix}$

To prove (42) let e=(u, f, b) be an element that is optimal for the useru and set S, i.e.

$\begin{matrix}{{h( {u,S} )} = {\min {\{ {{\vartheta_{u}Q_{u}},{\sum\limits_{n \in S}{r( {\underset{\_}{e},n} )}}} \}.}}} & (43)\end{matrix}$

Consider first the case that h(u, S)=Σ_(nεS)r(e, n)≦θ_(u)Q_(u). Usingthe inequality

$\begin{matrix}{{{{h( {u,T_{q}} )} \geq {\min \{ {{\vartheta_{u}Q_{u}},{\sum\limits_{n \in T_{q}}{r( {\underset{\_}{e},n} )}}} \}} \geq {\min \{ {{\vartheta_{u}Q_{u}},{\sum\limits_{n \in {T_{q}\bigcap S}}{r( {\underset{\_}{e},n} )}}} \}}} = {\sum\limits_{n \in {T_{q}\bigcap S}}{r( {\underset{\_}{e},n} )}}},} & (44)\end{matrix}$

we have that

$\begin{matrix}{{{{\sum\limits_{q}{\eta_{q}{h( {u,T_{q}} )}}} \geq {\sum\limits_{q}{\eta_{q}{\sum\limits_{n \in {T_{q}\bigcap S}}{r( {\underset{\_}{e},n} )}}}}} = {{{\sum\limits_{n \in S}{{r( {\underset{\_}{e},n} )}\underset{\underset{\geq 1}{}}{\sum\limits_{q:{n \in T_{q}}}\eta_{q}}}} \geq {\sum\limits_{n \in S}{r( {\underset{\_}{e},n} )}}} = {h( {u,S} )}}},} & (45)\end{matrix}$

which proves (42) for this case. Then, it remains to prove (42) whenh(u, S)=θ_(u)Q_(u)≦Σ_(nεS)r(e,n). In this case we can find a subset R⊂Ssuch that Σ_(nεR)r(e, n)≧θ_(u)Q_(u) but all its strict subsets A⊂Rsatisfy Σ_(nεA)r(e,n)≦θ_(u)Q_(u). Upon obtaining such an R, we candivide the cover {T_(q)} into two parts {T_(q)}_(qεI) ₁ : R⊂T_(q)∀qεI₁and the remaining sets of the cover are in {T_(q)}_(qεI) ₂ . Clearly, wehave that since Σ_(nεT) _(q) r(e,n)≧θ_(u)Q_(u)∀qεI₁,h(u,T_(q))=θ_(u)Q_(u)∀qεI₁. Consequently,

$\begin{matrix}{{{\sum\limits_{q}{\eta_{q}{h( {u,T_{q}} )}}} \geq {{\vartheta_{u}Q_{u}\underset{\underset{\beta}{}}{\sum\limits_{q:{q \in I_{1}}}\eta_{q}}} + {\sum\limits_{q:{q \in I_{2}}}{\eta_{q}{\sum\limits_{n \in {T_{q}\bigcap R}}{r( {\underset{\_}{e},n} )}}}}}} = {{\vartheta_{u}Q_{u}\beta} + {\underset{\underset{{\geq {\vartheta_{u}Q_{u}}}\;}{}}{\sum\limits_{n \in R}{r( {\underset{\_}{e},n} )}}{\sum\limits_{q \in {I_{2}:{n \in T_{q}}}}\eta_{q}}}}} & (46)\end{matrix}$

Notice that if β≧1 the desired inequality is already proved. On theother hand, β<1 then exploiting the fact that {η_(q),τ_(q)} is afractional cover of S, we can deduce that for each nεR, Σ_(qεI) ₂_(:nεT) _(q) η_(k)≧1−Σ_(qεI) ₁ _(:nεT) _(q) η_(q)≧1−β which using (46)yields the desired result.

We now offer an important result which is of independent interest. Ithas been proved that any fractionally sub-additive set function can beexpressed as a maximum over linear set functions. In particular, thismeans that there exist T linear functions g^((j)):{1, . . . , K}×N×IR₊,1≦j≦T such that

$\begin{matrix}{{{h( {u,R} )} = {\max\limits_{j}\{ {\sum\limits_{n \in R}{g^{(j)}( {u,n} )}} \}}},{{{{\forall{u \in \{ {1,\ldots \mspace{20mu},K} \}}}\&}R} \subseteq {N.}}} & (47)\end{matrix}$

The property in (47) leads to the following result.

Proposition 5. The combinatorial auction problem with fractionallysub-additive valuations can be re-formulated as the maximization of amonotonic sub-modular set function subject to one matroid constraint.Proof. Let us first define a set Ψ={(u, j): 1≦u≦K & 1≦j≦T} and a setfunction {tilde over (h)}: 2^(Ψ)→IR₊ as

$\begin{matrix}{{{\overset{\sim}{h}(A)} = {\sum\limits_{n \in N}{\max\limits_{{({u,j})} \in A}\{ {g^{(j)}( {u,n} )} \}}}},{\forall{A \subseteq {\Psi.}}}} & (48)\end{matrix}$

It can be shown that the set-function {tilde over (h)}(.) is a monotonicsub-modular set function. Then, we define a partition of Ψ as Ψ=∪_(u=1)^(K)Ψ_(u) where Ψ_(u)={(u, j): 1≦j≦T}, ∀u. Using this partition we candefine a family of subsets of Ψ, denoted by Ĩ, as

A⊂Ψ:|A∩Ψ _(u)|≦1∀u

AεĨ  (49)

It can be proved that the family Ĩ is an independence family and hence(Ψ,Ĩ) is a matroid, a partition matroid in particular. With these factsin hand we can obtain a reformulation of (41) as which yields thedesired proof.

$\begin{matrix}{\max\limits_{A:{A \in \overset{\sim}{I}}}{\overset{\sim}{h}(A)}} & (50)\end{matrix}$

□

The key benefit of this re-formulation is that (50) can be approximatelysolved with an ½ approximation using a simple greedy algorithm. Indeed,the interested reader will note that such a re-formulation was alreadyexploited in the iterative submodular algorithm. In this context we notethat an algorithm with ½ approximation was developed earlier forcombinatorial auction with valuations of the form in (47) (referred tothere as XOS valuations). However, the re-formulation in Proposition 5is more useful since algorithms for the maximization of submodularfunctions under a variety of constraints (such as multiple knapsacks,p-system) are now available. The caveat unfortunately is that T maydepend exponentially on which means that even the greedy algorithm maynot have polynomial complexity. Indeed, this happens to be the case forour per-user utility in (40) and hence obtaining a polynomial timegreedy algorithm seems challenging. Nevertheless, another approachdescribed below yields a polynomial time randomized algorithm.

We first state the following lemma follows directly from the obliviousrounding procedure developed in prior art.

Lemma 1. Given any feasible solution to the LP relaxation of (41), whichis

$\begin{matrix}{{\max\limits_{\underset{{{u \in {\{{1,\ldots \mspace{14mu},K}\}}},{R \subseteq N}}\}}{{\{{{\overset{\sim}{\chi}}_{u,R} \in {\{{0,1}\}}}\}}:}}{\sum\limits_{u \in {\{{1,\ldots \mspace{14mu},K}\}}}{\sum\limits_{R \subseteq N}{{h( {u,R} )}{\overset{\sim}{\chi}}_{u,R}}}}}{{{\sum\limits_{R:{n \in R}}{\sum\limits_{u}{\overset{\sim}{\chi}}_{u,R}}} \leq 1},{\forall{n \in N}}}{{{\sum\limits_{R}{\overset{\sim}{\chi}}_{u,R}} \leq 1},{\forall{u \in \{ {1,\ldots \mspace{14mu},K} \}}},}} & (51)\end{matrix}$

a solution feasible for (41) can be obtained such that its correspondingvalue is no less than a factor (1−1/e) times the one corresponding tothe solution feasible for the LP (51).

Separation oracle: Given any set of prices p_(n)εIR₊ ∀εN, for each useru a separation oracle returns the subset Ŝ=arg max_(S⊂N){h(u,S)−p(S)},where we let p(S)=Σ_(nεS)p_(n).

It seems intractable to construct such an oracle for our per-userutility function. Nevertheless, under the reasonable assumption that foreach element eεΩ and nεN the weighted rate r(e, n) is bounded by aconstant,⁵ it is possible to construct an approximate separation oracleas shown in the following result. We assume that the cardinality of theformat set F as well as the number of TPs B remain fixed. ⁵Thisassumption is reasonable since in many practical systems the maximuminput alphabet size is bounded above by 64 (corresponding to 64 QAM).

Proposition 6. There exists an approximate separation oracle that forarbitrarily chosen constants ε, δε(0, 1), any user u and any given setof prices p_(n)εIR₊, ∀nεN returns a set Ŝ such that

${{{h( {u,\hat{S}} )} - {p( \hat{S} )}} \geq {{( {1 - \varepsilon} ){\max\limits_{S \subseteq N}\{ {{h( {u,S} )} - {p(S)}} \}}} - \delta}},$

The complexity of the approximate separation oracle scales polynomiallyin each of

$K,|N|,{{\frac{1}{\in}\&}\mspace{14mu} \frac{1}{\delta}}$

Proof. Notice that since the cardinality of the format set F as well asthe number of TPs B remain fixed, it suffices to show the existence ofan approximate separation oracle that for any element e=(u, f, b)εΩ canreturn a set Ŝ such that

$\begin{matrix}{{{\min \{ {{\vartheta_{u}Q_{u}},{\sum\limits_{n \in S}{r( {\underset{\_}{e},n} )}}} \}} - {p( \hat{S} )}} \geq {{( {1 - \varepsilon} ){\max\limits_{S \subseteq N}\{ {{\min \{ {{\vartheta_{u}Q_{u}},{\sum\limits_{n \in S}{r( {\underset{\_}{e},n} )}}} \}} - {p(S)}} \}}} - {\delta.}}} & (52)\end{matrix}$

Towards this end, notice first that such an oracle can be triviallyobtained when Σ_(nεN)r(e, n)≦θ_(u)Q_(u) in which case we can indeeddetermine the optimal subset. Accordingly we suppose that Σ_(nεN)r(e,n)>θ_(u)Q_(u) and consider the problem

$\begin{matrix}{\max\limits_{S \subseteq N}{\{ {{\min \{ {{\vartheta_{u}Q_{u}},{\sum\limits_{n \in S}{r( {\underset{\_}{e},n} )}}} \}} - {p(S)}} \}.}} & (53)\end{matrix}$

Then, it can be seen that (53) can be solved by solving the twofollowing sub-problems:

$\begin{matrix}{{\max\limits_{S \subseteq {N:{{\sum\limits_{n \in S}{r{({\underset{\_}{e},n})}}} \leq {\vartheta_{u}Q_{u}}}}}\{ {\sum\limits_{n \in S}( {{r( {\underset{\_}{e},n} )} - p_{n}} )} \}}{and}} & (54) \\{\max\limits_{S \subseteq {N:{{\sum_{n \in S}{r{({\underset{\_}{e},n})}}} > {\vartheta_{u}Q_{u}}}}}{\{ {{\vartheta_{u}Q_{u}} - {p(S)}} \}.}} & (55)\end{matrix}$

The problem in (54) is the classical knapsack problem for which thereexists an FPTAS so that a solution Ŝ₁ with an approximation factor 1−εcan be recovered. On the other hand, (55) is equivalent to amin-knapsack problem. Here, to approximately solve (55), we leverage thefact that each r(e, n) is bounded above by a constant. This allows us touse the demand-based dynamic program for the knapsack problem andrecover in polynomial time a solution Ŝ₂ for which min {θ_(u)Q_(u),Σ_(nεŜ) ₂ r(e, n)}−p(Ŝ₂) is no less than max_(S⊂N:Σ) _(nεS) _(r(e,n)>θ)_(u) _(Q) _(u) {θ_(u)Q_(u)−p(S)}−δ. Then, by selecting the better optionamong Ŝ₁, Ŝ₂ we can obtain a set that offers the guarantee in (52). Theremaining part follows from the complexities of the FPTAS and thedemand-based dynamic program.Proposition 7. The LP (51) can be approximately solved in polynomialtime to obtain a solution whose value is no less than (1−ε){circumflexover (V)}^(LP)−δ, where {circumflex over (V)}^(LP) denotes the optimalvalue for the LP (51).Proof. Notice that the LP (51) has an exponential number of variables. Akey result that was discovered earlier in prior art was that such an LPcan be optimally solved in polynomial time given a separation oracle. Inparticular, the dual of this LP can be solved in polynomial time via theellipsoid method given a separation oracle. Then retaining only theconstraints encountered while solving the dual (which are polynomiallymany) we can get its primal LP counterpart which now has polynomiallymany variables and hence can be solved in polynomial time. This reducedvariable LP (which essentially is the same as (51) but where all but asmall subset of variables are fixed to zero) yields an optimal solutionto (51). This argument with some minor changes was also shown to workrecently for an β-approximate separation oracle, where β is theapproximation factor. Indeed, it is verified next that the same approachalso works for an approximate oracle of the form in (52). The keydifference is that upon using the ellipsoid method to solve the dual of(51) with our approximate separation oracle, we obtain a value{circumflex over (D)} upon convergence such that the optimal dual value(and hence the optimal primal value) lies in the interval

$\lbrack {{\hat{D} - \varepsilon^{\prime}},\frac{\hat{D} + \delta}{1 - \varepsilon}} \rbrack,$

where ε′>0 is the tolerance to decide the convergence of the ellipsoidmethod. Further, re-solving the modified dual wherein only theconstraints encountered in the first run of the ellipsoid method areretained, yields the same value {circumflex over (D)} upon convergenceand hence we can deduce that the true value of this modified dual andhence its primal counterpart also lies in the interval

$\lbrack {{\hat{D} - \varepsilon^{\prime}},\frac{\hat{D} + \delta}{1 - \varepsilon}} \rbrack.$

This primal counterpart which is the same as (51) but where all but asmall subset of polynomially many variables are fixed to zero, can besolved optimally in polynomial time to obtain a solution feasible for(51) and which yields a value in the aforementioned internal. Then,since this value, say {circumflex over (V)}, and the optimal value for(51), {circumflex over (V)}^(LP), both lie in

$\lbrack {{\hat{D} - \varepsilon^{\prime}},\frac{\hat{D} + \delta}{1 - \varepsilon}} \rbrack,$

we can deduce that {circumflex over (V)}≧(1−ε){circumflex over(V)}^(LP)−δ−ε′. Since the run time scales polynomially in each of

$\frac{1}{\in},{\frac{1}{\in^{\prime}}\mspace{14mu} {and}\mspace{14mu} \frac{1}{\delta}},$

we obtain the desired result.

We are now ready to offer our approximation algorithm for solving (38),which we refer to as the LP-rounding based approximation algorithm. TheLP-rounding based approximation algorithm consists of the followingsteps.

1. Approximately solve the LP (51) using the Ellipsoid method and theapproximate separation oracle

2. Use the oblivious rounding procedure to recover a solution feasiblefor (41).

3. Iteratively improve the solution while retaining feasibility withrespect to (38)

We note that the third step above can be done for instance using theapproach used in Algorithms II and III. In the following result we donot assume any such iteration, i.e., the approximation guarantee isobtained after the first two steps itself.Theorem 4. The LP-rounding based approximation algorithm yields asolution for (38) whose corresponding value is no less than

${{\frac{1}{B}( {1 - {1\text{/}e}} )( {1 - \varepsilon} ){\hat{V}}^{opt}} - \delta},$

where {circumflex over (V)}^(opt) denotes the optimal value for (38),and its complexity scales polynomially in each of

$K,|N|,{{\frac{1}{\in}\&}\mspace{14mu} \frac{1}{\delta}}$

Proof. Notice first that the optimal value for the LP in (51),{circumflex over (V)}^(LP), is an upper bound to the optimal value of(39) and hence upon invoking Proposition 3 we can conclude that

${\hat{V}}^{LP} \geq {\frac{{\hat{V}}^{opt}}{B}.}$

From Proposition 7 and

TABLE 2 Simulation Parameters Parameter Value used for evaluationNetwork and cell layout 19 sites, 3 sectors per site, wrap around;heterogeneous network with low power RRHs within the macrocell;uniformly distributed 4 RRHs per macrocell. Carrier frequency 2 GHzTransmission bandwidth 10M Hz Channel model Macrocell: ITU UMA with UEspeed 3 km/s; RRH: ITU UMi Antenna configuration ULA; Macro/RRH nT = 4;UE nR = 2 Traffic model Full buffer CQI/PMI feedback interval 5 TTIsFeedback delay 4 TTIs CSI feedback scheme per TP PMI/CQI/RI; fallbackserving TP CQI/PRI/RI Transmission scheme DPS/CSCB/SU-MIMO CoMP setthreshold 9 dB UE distribution configuration 4b with ⅓ macrocell UEs and⅔ RRH UEs; Number of UEs 30 UEs per cluster Channel estimation Ideal atUE; eNB approximates the channel based on UE feedbackLemma 1 we can conclude that a solution feasible for (39) and hence (38)can be recovered in polynomial time yielding a value no less than(1−1/e)(1−ε′){circumflex over (V)}^(LP)−δ′, which upon setting ε′=ε and

$\delta^{\prime} = \frac{\delta}{1 - {1\text{/}e}}$

then proves the theorem.

4 System Simulations

In this section we conduct a detailed evaluation of our algorithms. Ourfocus is on the practical gains that are possible by using thesescheduling algorithms over real networks.

In the following set of simulations we considered CoMP scenario 4b whichis particularly conducive to coordinated scheduling. Here 57 cells areemulated (with wraparound) and in each cell one Macro base station andfour remote radio heads are deployed. Each cluster covers a cell andthus comprises of M=5 TPs. 30 users on an average are dropped in eachcluster (cell) using a specific distribution. The major simulationassumptions are summarized in Table 2. The simulations were carried outfor a full buffer traffic model and the results are obtained overN_(TTI)=500 TTIs, where each TTI represents a scheduling interval.

4.1 Channel Feedback

In FDD systems the central scheduler must rely on the feedback from theusers in order to obtain estimates or approximations of their respectivedownlink channels. Since the uplink resources available for suchfeedback are limited the following low overhead feedback signallingscheme is supported.

-   -   A measurement set of TPs, which is any subset of {1, . . . , M},        is configured separately for each user based on slowly varying        large-scale fading parameters such as path-loss, shadowing etc.        Each user only estimates channels from TPs in its measurement        set whereas the TPs not in its measurement set together with        those outside the cluster are treated as interferers or        un-coordinated TPs. The idea is that depending on its location        the user may receive useful signal strength (above a        configurable threshold) only from a few TPs in the cluster.    -   For each TP in its measurement set, the user computes the        associated per-point channel state information (CSI) as follows.        It first estimates the corresponding channel on each subband        (which in turn comprises of a set of contiguous RBs) and then        “whitens” it. This whitening operation is done via a linear        filter obtained using the interference covariance and accounts        for the interference the user will see from the un-coordinated        TPs.    -   Each whitened channel matrix is quantized into a set of good        directions using a matrix drawn from a precoding codebook and a        set of gains. The number of directions (or columns in the        matrix) is referred to as the rank and is invariant across all        sub-bands. The user then reports the rank, the per-subband        selected matrix along with the per-subband gains, which together        constitute the per-point CSI for that TP.    -   In addition, the user also reports a “fallback” CSI which is        computed by estimating the channel from the anchor TP and        whitening it after considering interference from all other TPs.        This fall back CSI is provided to allow simple un-coordinated        per-point scheduling. One approach to reduce the feedback, which        is investigated here, is to further impose a common rank        restriction across all TPs wherein a user first computes its        fallback CSI and then computes the other per-point CSI under the        restriction that the rank contained in each per-point CSI be        identical to that in the fallback CSI.

The size of a sub-band (frequency granularity) and the periodicity (timegranularity) of feedback are configurable parameters. We assumed afairly fine granularity by setting a sub-band size of 5 RBs and aperiodicity of 4 ms. The central scheduler collects all the reportedfeedback and uses it to construct channel approximations. In particular,for each user, for each TP in that user's measurement set and for eachsubband, the central scheduler collects the corresponding reported gainsin a diagonal matrix D and uses the associated precoder matrix, say V,to approximate the channel as D^(1/2)V†. Note here that V issemi-unitary (V†V=I) so that a symbol transmitted along the i^(th)column of V will see a gain of d_(i). This channel approximation is usedfor all RBs in that sub-band. The channels from all TPs not in theuser's measurement set are assumed to be zero. One other aspect thatneeds to be emphasized is the choice of receiver at each user since ithas an impact on the gains that can be achieved via CoMP schemes. Wefirst assume a simple receiver at each user wherein the interferencecovariance is estimated by just measuring the interference powerper-receive antenna which is equivalent to restricting the interferencecovariance estimate to be a diagonal matrix. This receiver is referredto as the MMSE option-1 receiver in the standard and is used as thebaseline receiver in all evaluations. Later we will assume a moreadvanced receiver. In all the following simulations the per-pointscheduling scheme is used as the baseline in which the scheduling isdone separately for each TP using the fallback CSI and an algorithm thatis obtained by specializing Algorithm II to one iteration and a singleTP. Further, the aggressive pruning in Algorithms II and III was usedfor all cases.

4.2 Results and Observations

We send forth our first results in Tables 3 and 4 where we employ theiterative sub-modular algorithm and the iterative format balancingalgorithm, respectively, for coordinated scheduling. We note that aserving TP balancing step is also incorporated in Algorithm III when theselected CoMP scheme is CDPS. In each case the relative percentage gainsare over the baseline. From Tables 3 and 4 it is seen that CoMP schemesyield a catastrophically poor performance compared to the baselineper-point scheduling. It would seem that inspite of provisioningadditional feedback from the users to enable CoMP schemes, the systemincurs a loss which is highly undesirable.

Observation 1. The performance of CoMP schemes is highly sensitive tothe quality of feedback received from the users.

Fortunately, another form of feedback is also available in the form ofACK/NACK feedback that is received from each user. This feedback hasbeen successfully used in the traditional single cell scheduling.

TABLE 3 Spectral Efficiency (bps/Hz) of CoMP schemes with iterativesubmodular algorithm. Scheduling scheme DPS CDPS CS/CB Baseline cellaverage 1.9187 1.9238 1.9955 2.0858 (−8.01%) (−7.77%) (−4.33%) (0%) 5%cell-edge 0.0281 0.0295 0.0292 0.0443 (−36.57%) (−33.41%) (−34.09%) (0%)Actual BLER 34.97% 34.81% 31.98% 25.78% Empty RB ratio    8%    8%    0%   0%

TABLE 4 Spectral Efficiency (bps/Hz) of CoMP schemes with iterativeformat balancing algorithm. Scheduling scheme DPS CDPS CS/CB Baselinecell average 1.9202 1.9239 1.9909 2.0858 (−7.94%) (−7.76%) (−4.55%) (0%)5% cell-edge 0.0264 0.0280 0.0291 0.0443 (−40.41%) (−36.79%) (−34.31%)(0%) Actual BLER 34.86% 34.82% 32.53% 25.78% Empty RB ratio    8%    8%   0%    0%We leverage this feedback to refine the channel approximations at thecentral schedular in the following manner. For each user k and a giventransmission hypotheses involving user k, the approximations of allchannels seen by user k from TPs in its measurement set are obtained asbefore. Then, on each subband the channel approximation corresponding tothe TP involved in serving data to user k (if any, under the givenhypotheses) is scaled by a factor c_(k) which represents the correctionfactor associated with user k. This scaling factor is continuallyupdated based on the sequence of ACK/NACKs received from that user.While the update procedure is proprietary, it follows the principle thatevery ACK increases the factor whereas every NACK decreases it.

We offer our results incorporating ACK/NACK based refinement in Tables 5and 6.

From Tables 5 and 6 we see that the performance of CoMP schemes hasdramatically improved due to the ACK/NACK based refinement and moreimportantly, CoMP schemes now yield their promised cell-edge gains.Indeed very significant cell edge gains are obtained by all three CoMPschemes with the DPS and CDPS gains being outstanding. Notice that inboth the latter schemes the empty (or muted) RB ratio is high whichmeans that these schemes exploit RB silencing (or muting) moreaggressively to reduce interference.

Observation 2. Exploiting ACK/NACK feedback to refine channelapproximations pays rich dividends and is necessary to realize CoMPgains.

Henceforth, unless otherwise mentioned, in all the following simulationswe exploit the ACK/NACK

TABLE 5 Spectral Efficiency (bps/Hz) of CoMP schemes with iterativesubmodular algorithm and ACK/NACK refinement. Scheduling scheme DPS CDPSCS/CB Baseline cell average 2.3981 2.3988 2.4461 2.4297 (−1.30%)(−1.27%) (0.67%) (0%) 5% cell-edge 0.0976 0.0962 0.0898 0.0806 (21.09%)(19.35%) (11.41%) (0%) Actual BLER 6.02% 6.01% 5.54% 5.13% Empty RBratio   7%   6%   0%   0%

TABLE 6 Spectral Efficiency (bps/Hz) of CoMP schemes with iterativeformat balancing algorithm and ACK/NACK refinement. Scheduling schemeDPS CDPS CS/CB Baseline cell average 2.4006 2.3974 2.4617 2.4297(−1.20%) (−1.33%) (1.32%) (0%) 5% cell-edge 0.0962 0.0953 0.0856 0.0806(19.35%) (18.24%) (6.20%) (0%) Actual BLER 6.00% 6.01% 5.55% 5.13% EmptyRB ratio   7%   7%   0%   0%feedback. We now investigate a more expanded feedback scheme wherein thecommon fallback rank restriction is removed. We remark that by imposingthe fallback rank restriction we bias a CoMP UE (i.e., a user with morethan one TP in its measurement set) to report per-point CSI with a lowerrank. This is because the fallback CSI is computed under the assumptionof interference from all non-anchor TPs and hence will choose a lowerrank. Put another way, a CoMP user is likely to be a cell-edge userunder fallback single-point scheduling and hence will support a lowerrank. Clearly, imposing this fallback rank restriction on all per-pointCSI will result in disabling higher-rank transmission for a CoMP user,which might potentially lower the rate. However, it also has a keyadvantage. Note that under rank restriction for each per-point CSI, theuser first determines the optimal un-quantized channel approximation ofthe given rank and then quantizes it. Then, an important fact is thatgiven a fixed quantization load (decided by the codebook size)quantization error is smaller for lower ranks. The net effect of this isthat the first few dominant singular vectors (which represent preferreddirections) along with the corresponding singular values are moreaccurately reported by the user at the expense of not reporting theremaining ones at all. In the case without rank restriction the userwill typically pick a larger set of singular vectors to quantize. Thisresults in the central scheduler knowing more directions and associatedgains, albeit more coarsely.

We provide the results to highlight the impact of rank restriction inTable 7. For brevity we consider two CoMP schemes and the iterativesubmodular algorithm. From the results we see that fallback rank

TABLE 7 Spectral Efficiency (bps/Hz) of CoMP schemes with iterativesubmodular algorithm, ACK/NACK refinement, with (RR = 1) and without (RR= 0) rank restriction. Scheduling DPS DPS CS/CB CS/CB scheme (RR = 1)(RR = 0) (RR = 1) (RR = 0) cell average 2.3981 2.3579 2.4461 2.4397(1.70%) (0.26%) 5% cell-edge 0.0976 0.0955 0.0898 0.0902 (2.20%)(−0.44%) Actual BLER 6.02% 7.08% 5.54% 6.10% Empty RB ratio   7%   7%  0%   0%

TABLE 8 Spectral Efficiency (bps/Hz) of CoMP schemes with iterativesubmodular algorithm, ACK/NACK refinement, rank restriction and MMSE-IRCreceiver. Scheduling scheme DPS CDPS CS/CB Baseline cell average 2.7172.7148 2.7512 2.8011 (−3.00%) (−3.08%) (−1.78%) (0%) 5% cell-edge 0.12880.1271 0.1112 0.1058 (21.74%) (20.13%) (5.10%) (0%) Actual BLER 5.28%5.30% 5.12% 4.78% Empty RB ratio   9%   8%   0%   0%restriction results in almost no degradation which suggests thataccurately knowing a fewer directions from each CoMP user allows thenetwork to better manage interference thereby offsetting the loss due todisabling higher rank transmission to those users.Observation 3. Rank restriction is a useful feedback reduction strategyunder limited quantization load.

Recall that hitherto we have assumed a simple receiver at each user. Wenow consider a more advanced receiver at each user in which theinterference covariance is estimated without any restrictions. Thisresulting receiver is referred to as the MMSE-IRC receiver. Our resultsare reported in Tables 8 and 9 where we note that both ACK/NACK basedrefinement and rank restriction have been imposed. An interestingobservation is that while the performance of all schemes hassubstantially improved compared to their counterparts in Tables 5 and 6,the relative gains over the baseline per-point scheduling havedecreased. This is due to the fact that the scenario favorable for largeCoMP gains over per-point scheduling is one where the central schedulerhas good network CSI but the user receivers have limited interferencerejection capabilities. On the other hand, the worst scenario would bethe one where the network CSI at the scheduler is poor but the usershave powerful receivers in which case CoMP schemes would be detrimental.The scenario emulated in Tables 8 and 9 is more closer to the lattercase since compared to the one in Tables 5 and 6, the total feedbackoverhead is identical but the receivers are more robust. We thus havethe following observation

TABLE 9 Spectral Efficiency (bps/Hz) of CoMP schemes with iterativeformat balancing algorithm, ACK/NACK refinement, rank restriction andMMSE-IRC receiver Scheduling scheme DPS CDPS CS/CB Baseline cell average2.7168 2.7135 2.7656 2.0811 (−3.01%) (−3.13%) (−1.27%) (0%) 5% cell-edge0.1289 0.1288 0.1087 0.1058 (21.83%) (21.74%) (2.74%) (0%) Actual BLER5.28% 5.28% 5.11% 4.78% Empty RB ratio   9%   8%   0%   0%

TABLE 10 Spectral Efficiency (bps/Hz) of CoMP schemes with iterativesubmodular algorithm, MMSE-IRC receiver, ACK/NACK refinement, with (RR= 1) and without (RR = 0) rank restriction. Scheduling DPS DPS CS/CBCS/CB scheme (RR = 1) (RR = 0) (RR = 1) (RR = 0) cell average 2.71702.6700 2.7512 2.7328 (1.76%) (0.67%) 5% cell-edge 0.1284 0.1274 0.11120.1081 (1.10%) (2.87%) Actual BLER 5.28% 6.00% 5.12% 5.70% Empty RBratio   9%   9%   0%   0%Observation 4. Improving user receivers without commensurateenhancements in CSI feedback leads to smaller CoMP gains.

In Table 10 we simulate a scenario without the ACK/NACK basedrefinement. The results demonstrate that ACK/NACK based refinement isindeed necessary and thus the observation 2 is true even with morepowerful user receivers.

Finally, in Table 11 we retain ACK/NACK based refinement but remove therank restriction. It is seen that observation 3 holds true even forthese robust receivers.

[Algorithm I: Format Balancing Algorithm]  1. Initialize

 = φ, ∀ n ∈ 

 2. FOR each n ∈ 

 DO  3. Solve  $\max\limits_{\underset{\_}{ \Subset \Omega}}{\mspace{11mu} {r( {,\; n} )}}$(56)  4. Denote the obtained solution by

.  5. END FOR  6. FOR each user u DO  7. FOR each format f DO  8. Set

 (u, f) = 0  9. FOR each RB n for which ∃ e ∈

: u _(e) = u & f _(e) ≧ f DO 10. Set

 = 

 \ e and e′ = (u, f, b _(e) ) 11. Compute r _(e) _(′) (

 ∪ e′, n) and increment

 (u, f) =

 (u, f) + r _(e) _(′) (

 ∪ e′, n) 12. END FOR 13. END FOR 14. Determine {circumflex over (f)} =arg max_(f) {

 (u, f)} 15. FOR each RB n for which ∃ e ∈ 

: u _(e) = u & f _(e) ≧ {circumflex over (f)} DO 16. Set e′ = (u,{circumflex over (f)}, b _(e) ) and expand

 = 

 ∪ e′ 17. END FOR 18. Output the final scheduling decisions

 ∀ n ∈ 

[Algorithm II: Iterative Submodular Algorithm]  1.Initialize    = Ω,   2. WHILE (done = false) and (Iter ≦ IterMax) 3.

 = φ, 

  = 

 4. REPEAT  5. Solve  $\mspace{14mu} g\mspace{14mu} ( {{\bigcup\underset{\_}{e}}\{ \; \}_{{n\varepsilon}}} )$(57) and let  

, {circumflex over (v)} denote the optimal solution and the optimalvalue.  6. If {circumflex over (v)} > 0 THEN update  

 → 

 ∪

,  

 → 

 \ 

. (58)  7. END IF  8. UNTIL {e ∈

 :

 ∪ e ∈

 } = φ or {circumflex over (v)} = 0  9. IF

 = φ THEN set done = true 10. ELSE 11. Update Iter → Iter + 1. 12. FOReach n ∈

 DO 13. $\mspace{14mu} {\begin{matrix}{{{Determine}\mspace{14mu} {\underset{\_}{ê}}^{(n)}} = {\arg \mspace{11mu} \mspace{11mu} \hat{r}\; ( {e,,n} )\mspace{14mu} {and}\mspace{14mu} {let}\mspace{14mu} {\hat{v}}^{(n)}}} \\{{be}\mspace{14mu} {the}\mspace{14mu} {corresponding}\mspace{14mu} {optimal}\mspace{14mu} {{value}.}}\end{matrix}\quad}$ 14. IF {circumflex over (v)}^((n)) > 0 THEN 15.Increment

 =

 ∪  

16. END IF 17. END FOR 18. END IF 19. Prune

 using the obtained set 

20. END WHILE 21. Output {

 }, n ∈ 

[Algorithm III: Iterative Format Balancing Algorithm for CS/CB or DPS] 1.${{{Initialize}\mspace{11mu} }\; = \; \underset{\_}{\Omega}},\{ {,{{done} = {{{false}\mspace{14mu} {and}\mspace{14mu} {Iter}} = 1.}}} $ 2. WHILE (done = false) and (Iter ≦ IterMax)  3. Set done = true.  4.FOR each n ∈ 

 DO  5. Solve  $\mspace{11mu} \overset{\sim}{r}\; ( {\underset{\_}{e},,n} )$(59)  6. Denote the obtained solution by  

 and the value by {circumflex over (v)}^((n)).  7. END FOR  8. FOR eachuser u DO  9. FOR each format f DO 10. Set

(u, f) = 0 11.${{{{{FOR}\mspace{14mu} {each}\mspace{14mu} {RB}\mspace{14mu} n\mspace{14mu} {for}\mspace{14mu} {which}\mspace{14mu} {\hat{v}}^{(n)}} > 0}\&}\mspace{14mu} u_{{\underset{\_}{ê}}^{(n)}}} = {u\mspace{14mu} {DO}}$12.${{Set}\mspace{14mu} \underset{\_}{e}} = ( {u,f,b_{{\underset{\_}{ê}}^{(n)}}} )$13. IF e ∈ 

  THEN 14. Increment

 (u, f) = 

 (u, f) + {tilde over (r)}(e,

, n) 15. END IF 16. END FOR 17. END FOR 18. Determine {circumflex over(f)} = arg max_(f) {

 (u, f)} 19.${{{{{FOR}\mspace{14mu} {each}\mspace{14mu} {RB}\mspace{14mu} n\mspace{14mu} {for}\mspace{14mu} {which}\mspace{14mu} {\hat{v}}^{(n)}} > 0}\&}\mspace{14mu} n_{{\underset{\_}{ê}}^{(n)}}} = {u\mspace{14mu} {DO}}$20.${{Set}\mspace{14mu} {\underset{\_}{e}}^{\prime}} = ( {u,\hat{f},b_{{\underset{\_}{ê}}^{(n)}}} )$21. IF {tilde over (r)}(e′,

, n) > 0 THEN 22. Expand

 =

 ∪ e′ 23. Set done = false. 24. END IF 25. END FOR 26. END FOR 27.Prune 

 using the obtained set 

28. END WHILE

TABLE 11 Spectral Efficiency (bps/Hz) of CoMP schemes with iterativesubmodular algorithm, MMSE-IRC receiver, rank restriction but withoutACK/NACK refinement. Scheduling scheme DPS CDPS CS/CB Baseline cellaverage 2.3956 2.4026 2.4711 2.6244 (−8.72%) (−8.45%) (−5.84%) (0%) 5%cell-edge 0.0729 0.0732 0.0754 0.0947 (−23.02%) (−22.70%) (−20.38%) (0%)Actual BLER 26.13% 25.92% 23.59% 16.76% Empty RB ratio    9%    9%    0%   0%

Further System Details B I. Introduction

In order to accommodate the explosive growth in data traffic networkoperators are increasingly relying on cell splitting, wherein multipletransmission points (TPs) are placed in a cell traditionally covered bya single macro base station. Each such transmission point can be a highpower macro enhanced base-station but is more likely to be a low-powerremote radio head of more modest capabilities. The networks formed bysuch disparate transmission points are referred to as heterogeneousnetworks (a.k.a. HetNets) and are rightly regarded as the future of allnext generation wireless networks. In the HetNet architecture the basiccoordination unit is referred to as a cluster which consists of multipleTPs. Coordinated resource allocation within a cluster must beaccomplished at a very fine time scale, typically once everymillisecond. This in turn implies that all TPs within each cluster musthave fiber connectivity and hence the formation of clusters (a.k.a.clustering) is dictated by the available fiber connectivity among TPs.On the other hand, coordination among different clusters is expected tobe done on a much slower time-scale. Consequently, each user can beassociated with only one cluster and the association of users toclusters needs to be done only once every few seconds.

In this paper our interest is on the dynamic coordination within eachcluster. Since user association and clustering happen on time scaleswhich are several orders of magnitude coarser, we assume them to begiven and fixed. The design of joint resource allocation within acluster of multiple TPs has been considered in depth in recent years.These techniques range from assuming global knowledge of user channelsstates and their respective data at a central processor, therebyconverting the cluster into one broadcast channel with global knowledge,to one where only user channel states are shared among TPs in a clusterso that each user can be served by only one TP but downlink transmissionparameters (such as beam-vectors and precoders) can still be jointlyoptimized. Our goal in this work is to verify whether the wisdom accruedfrom all these works about substantial performance gains being possibleif interference is managed via coordinated resource allocation is validover real HetNets. The challenges over realistic networks are threefold,namely, (i) the need for low complexity resource allocation algorithmsthat can be implemented in very fine time-scales (ii)incomplete/inaccurate channel feedback from the users and (iii) realpropagation environments. Clearly, since no such real HetNets have yetbeen deployed, we have to rely on accurate modeling. Here, to capturethe latter two challenges, we rely on the emulation of such networks asspecified by the 3GPP LTE standards body which has considered HetNetdeployments in a very comprehensive manner. The simplest “baseline”approach then to manage dynamic coordination within a cluster is toassociate each user with one TP within the cluster from which itreceives the strongest average signal power (referred to as its “anchor”TP), and then perform separate single-point scheduling for each TP withfull reuse. While this approach might appear simplistic and deficientwith respect to degree of freedom metrics, over realistic networks itcaptures almost all of the average spectral efficiency gains promised bycell splitting. Indeed, the expectation from more sophisticated jointscheduling schemes in a cluster is mainly to achieve significant gainsin the 5-percentile spectral efficiency while retaining the averagespectral efficiency gains of the baseline. Towards realizing thisexpectation, we formulate a joint resource allocation problem andproceed to develop a constant-factor approximation algorithm based on anovel approach that combines submodular welfare maximization and atechnique referred to as format balancing. The key aspect is that theformulated resource allocation problem can accommodate importantpractical constraints and specific choices of transmission parameters.Consequently, the designed algorithm is directly applicable topractically important scenarios and indeed shows promising gains whenevaluated under realistic conditions.

II. System Model

We consider the downlink in a HetNet with universal frequency reuse andfocus on a cluster of B coordinated TPs which can simultaneouslytransmit on N orthogonal resource blocks (RBs) during each schedulinginterval. Each RB is a bandwidth slice and represents the minimumallocation unit. Together, these B TPs serve a pool of K active users.Each TP as well as each user can be equipped with multiple antennas. Weassume a typical HetNet scenario (as defined in the 3GPP LTE Rel. 11)wherein these B TPs are synchronized and can exchange messages over afiber backhaul. Next, the signal received by a user k on RB n can bewritten as

$\begin{matrix}{{{y_{k}(n)} = {{\sum\limits_{j = 1}^{B}\; {{H_{k,j}(n)}{x_{j}(n)}}} + {z_{k}(n)}}},} & (1)\end{matrix}$

where H_(k,j)(n) models the MIMO channel between TP j and user k on RB n(which includes small-scale fading, large-scale fading and pathattenuation), while z_(k) (n) is the additive circularly-symmetricGaussian noise vector and x_(j)(n) denotes the signal vector transmittedby TP j on the n^(th) RB.¹ Considering the signal transmitted by a TP,we impose the common restriction that each TP is allowed to serveat-most one user on each RB. This restriction provides robustnessagainst imperfect and coarse channel feedback from the users. Then, thesignal transmitted by TP q on RB n can then be expressed as

x _(q)(n)=W _(q,n)(n)b _(q,n)(n),  (2)

where b_(q,n)(n) is the complex symbol vector transmitted by TP q on RBn intended for some user u using the precoding matrix W_(q,n)(n) whichsatisfies a norm (power) constraint. Notice that due to the broadcastnature of the wireless channel, the signal intended for a usertransmitted by some TP on an RB is received as interference by all otherco-scheduled users on that RB. This factor significantly complicates thescheduling problem since it is no longer meaningful to define a per-userutility that depends on the resources allocated to that user alone.¹Notice that the model in (1) holds for the case of orthogonalfrequency-division-multiple access (OFDMA) if the maximum signalpropagation delay is within the cyclic prefix.

In order to abstract out the details while retaining usefulness, weadopt the notion of a transmission hypothesis. In particular, we definee=(u, f, b) as an element, where u: 1≦u≦K denotes a user, fεF={1, . . ., J} denotes a format drawn from a finite set F of such formats having acardinality J=|F| and b:1≦b≦B denotes a transmission point (TP). Eachsuch element e=(u, f, b) represents a transmission hypothesis, i.e., thetransmission from TP b using format f intended for user u. Next, we letΩ={e=(u, f, b): 1≦u≦K, fεF, 1≦b≦B} denote the ground set of all possiblesuch elements. For any such element we adopt the convention that

e =(u,f,b)

u _(e) =u,f _(e) =f,b _(e) =b.

Then, letting N={1, . . . , N} denote the set of RBs, we let r:2 ^(Ω)×N→IR₊ denote the weighted sum rate utility function. For any subset A ⊂Ω and any RB nεN, r(A, n) yields the weighted sum rate obtained upontransmission using the hypotheses in A on RB n. The hypotheses in A cancontain multiple hypothesis, for instance selecting A={e,e′} on an RB nimplies that on RB n, TP b _(e) will transmit a signal intended for useru _(e) using format f _(e) and simultaneously TP b _(e′) will transmit asignal intended for user u _(e′) using format f _(e′). The weightassociated with each element e (or equivalently user u _(e) ) is aninput to the scheduler and is in turn updated using the resultingscheduling decision. In order to disallow the possibility of the same TPserving multiple users on the same RB as well as the possibility of thesame user receiving data from multiple TPs on the same RB,² we adopt theconvention that

∃ e≠eεA:u _(e) =u _(e′) or b _(e′) =b _(e′)

r( A,n)=0.  (3)

²This latter restriction is required since enabling reception of datasimultaneously from multiple TPs on the same frequency requiresadditional feedback from the users to allow coherent combining, which isnot available.

Further, for any A ⊂ Ω we can expand

$\begin{matrix}{{{r( {\underset{\_}{A},n} )} = {\underset{\underset{\_}{e} \in \underset{\_}{A}}{\Sigma}{r_{\underset{\_}{e}}( {\underset{\_}{A},n} )}}},} & (4)\end{matrix}$

where r _(e) (A, n) is the weighted rate obtained for element e orequivalently the user u _(e) using the hypotheses in A on RB n and wherewe set r _(e) (A, n)=0∀eεA whenever r(A, n)=0. Notice that uponselecting any hypotheses in A on any RB n, we have an interferencechannel formed by the TPs and users contained in those hypotheses. Then,any pre-determined rule to compute the weighted sum rate can be used.Throughout this paper, we will assume that the weighted sum rate utilityfunction satisfies a natural sub-additivity assumption which says thatthe rates of elements in a set will not decrease if some elements areexpurgated from that set. In particular, for any subset A ⊂ Ω and anyelement eεA, defining C=A\e we assume that for each nεN

r _(e″)( C,n)≧r _(e″)( A,n),∀ e″εC.  (5)

We assume that any one of the two following coordinated multi-point(CoMP) schemes is selected for each user. We emphasize that theassociation of a user with a CoMP scheme is pre-determined and fixed.

Coordinated Silencing/Coordinated Beamforming (CS/CB): A user associatedwith this scheme can be served data only by its pre-determined “anchor”TP so that no real-time sharing of that user's data among TPs is needed.Thus, for a CS/CB user u, any eεΩ with u _(e) =u must satisfy that TP b_(e) is the anchor TP of u.

Dynamic Point Selection (DPS): A user associated with this scheme can beserved by any TP on any RB.

Notice that for both the CoMP schemes interference mitigation can beachieved via proper user and format selection. In addition, DPS allowsfor an increase in received signal strength by exploiting short-termfading via per-RB serving TP selection, where serving TP means the TPthat serves data to the user. Then, letting Q_(u),θ_(u) denote thebuffer size (in bits) of user u and its scheduling weight³,respectively, we formulate the optimization

$\begin{matrix}{{{\max\limits_{\substack{\{{\chi_{\underset{\_}{A},n} \in {{\{{0,1}\}}\text{:}}} \\ {{\underset{\_}{A} \subseteq \underset{\_}{\Omega}},{n \in N}}\}}}{\underset{{u\text{:}u} \in {\{{1,\cdots,K}\}}}{\Sigma}\min \{ {{\underset{{\underset{\_}{e} \in {\underset{\_}{\Omega}\text{:}u_{\underset{\_}{e}}}} = u}{\Sigma}\underset{\underset{\_}{A} \subseteq {\underset{\_}{\Omega}\text{:}\underset{\_}{e}} \in \underset{\_}{A}}{\Sigma}\underset{n \in N}{\Sigma}{r_{\underset{\_}{e}}( {\underset{\_}{A},n} )}\chi_{\underset{\_}{A},n}},{\nu_{u}Q_{u}}} \} \underset{\underset{\_}{A} \subseteq \underset{\_}{\Omega}}{\Sigma}\chi_{\underset{\_}{A},n}}} \leq 1},{{\forall n};{{( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{A},n}} )( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{B},n}} )} = 0}},{\forall\underset{\_}{A}},{\underset{\_}{B} \subseteq {\underset{\_}{\Omega}\text{:}{\exists{\underset{\_}{e} \in \underset{\_}{A}}}}},{{{{{\underset{\_}{e}}^{\prime} \in \underset{\_}{B}}\&}u_{\underset{\_}{e}}} = u_{{\underset{\_}{e}}^{\prime}}},{{f_{\underset{\_}{e}} \neq f_{{\underset{\_}{e}}^{\prime}}};}} & (6)\end{matrix}$

problem given by (6). Note that in (6) the objective functionincorporates the finite buffer limits, whereas the first constraintensures that at-most one transmission hypotheses is selected on each RB.The second constraint ensures that each scheduled user is assigned onlyone format. For a given number of users (K), TPs (B), RBs (N) andformats (J), an instance of (6) is a set of user weights and buffersizes {θ_(u),Q_(u)}_(u=1) ^(K) together with the set of all weighted sumrate utility values for all possible hypotheses on all RBs. Beforeproceeding to design an approximation algorithm for (6), we consider aspecific example of a format along with the rule to compute the weightedsum rate. A format can for instance be defined as the number of symbolstreams assigned, in which case on any RB and for a given transmissionhypotheses, we have an interference channel where the number of streamsfor each transceiver link is now given. The rule to evaluate theweighted sum rate can then be the one which assumes a Gaussian inputalphabet for each transceiver link and a transmit precoding method suchas the one based on interference alignment. Notice that the constraintof at-most one format per scheduled user then captures the mainconstraint in the LTE standard which is that each scheduled user beassigned the same number of streams on all its assigned RBs. Our firstresult is that (6) is unlikely to be optimally solved by a low(polynomial) complexity algorithm. It follows upon reducing (6) to twospecial cases and exploiting their known hardness. ³Without loss ofoptimality, we can assume that the user weights are normalized to lie in[0, 1].Theorem 1. The optimization problem in (6) is NP hard. Specifically, forany fixed N≧1 & J≧2, in (6) is strongly NP hard. For any fixed B≧1 &J≧1, (6) is APX hard.

Theorem 1 implies that not only is the existence of an efficient optimalalgorithm for (6) highly improbable, an exponential complexity withrespect to B is the likely price we have to pay in order to obtain aapproximation factor independent of B. Here, we adopt an iterativeframework to design an approximation algorithm which will make thecomplexity polynomial in even B but will introduce a penalty of 1/B inthe approximation guarantee. Accordingly, we introduce another simplerproblem given by (7) The relation between the weighted sum ratesobtained using the optimal solutions to (6) and (7) is given by thefollowing result.

$\begin{matrix}{{{\max\limits_{\substack{\{{\chi_{\underset{\_}{e},n} \in {{\{{0,1}\}}\text{:}}} \\ {{\underset{\_}{e} \subseteq \underset{\_}{\Omega}},{n \in N}}\}}}{\underset{{u\text{:}u} \in {\{{1,\cdots,K}\}}}{\Sigma}\min \{ {{\underset{{\underset{\_}{e} \in {\underset{\_}{\Omega}\text{:}u_{\underset{\_}{e}}}} = u}{\Sigma}\underset{n \in N}{\Sigma}{r( {\underset{\_}{e},n} )}\chi_{\underset{\_}{e},n}},{\nu_{u}Q_{u}}} \} \underset{\underset{\_}{e} \subseteq \underset{\_}{\Omega}}{\Sigma}\chi_{\underset{\_}{e},n}}} \leq 1},{{\forall n};{{( {\underset{n \in N}{\Sigma}\chi_{\underset{\_}{e},n}} )( {\underset{n \in N}{\Sigma}\chi_{{\underset{\_}{e}}^{\prime},n}} )} = 0}},{\forall\underset{\_}{e}},{{{\underset{\_}{e}}^{\prime} \subseteq {\underset{\_}{\Omega}\text{:}u_{\underset{\_}{e}}}} = u_{{\underset{\_}{e}}^{\prime}}},{{f_{\underset{\_}{e}} \neq f_{{\underset{\_}{e}}^{\prime}}};}} & (7)\end{matrix}$

Proposition 1. The optimal solution to (7) is feasible for (6) andyields a value that is no less than a factor 1/B times that yielded bythe optimal solution to (6).

Proof: We first assume that the CoMP scheme associated with all users isCS/CB. Consider then an optimal solution to (6), say {Â ^((n))}_(nεN),and for that solution let G_(b)′ denote the set of users served by TP bwhere b=1, . . . , B. Since CS/CB is used for all users, we can deducethat these sets are non overlapping, i.e., G_(k)′∩G_(j)′=φ, ∀k≠j.Further, the overall utility can be expanded as Σ_(b=1) ^(B)R_(b), whereR_(b) is the weighted sum of rates of all users in G_(b)′, wherein theper-user finite buffer constraints are included. Next, consider a TP band suppose that on each RB nεN a genie removes the interference causedto the user being served by TP b from co-scheduled transmissions byother TPs. Invoking the property in (5), we can see the resultingweighted sum rate {circumflex over (R)}_(b) will be at-least as large asR_(b). However, {circumflex over (R)}_(b) can be achieved by aparticular solution to (7) derived from {Â ^((n))}_(nεN), wherein onlythe element containing a user in G_(b)′ is retained in each Â ^((n))(notice that there can only be one such element in each Â ^((n))) andthe others are expurgated. This implies that the optimal solution to (7)yields a value that is an upper-bound to each {circumflex over (R)}_(b),b=1, . . . , B, which in turn allows us to conclude that the theorem istrue. Now consider the general case where DPS is adopted as the CoMPscheme for some users while CS/CB is adopted for the remaining ones. Inthis case, let us split each DPS user u into B users u^((i)), i=1, . . ., B with identical weights, channels and queue sizes and with theunderstanding that the i^(th) such user is a CS/CB user whose anchor isTP i so that it can only be served data by TP i. Let us collect thisenlarged pool of {tilde over (K)}>K users and pose the problem in (6)over this larger pool, wherein all users are CS/CB users and the bufferconstraint is imposed separately on each user. Clearly the optimal valueof the latter problem is an upper bound on that of the original one withK users. Moreover, upon noticing that each TP can be the anchor of nomore than K users from the enlarged pool and invoking the arguments madebefore, we can assert that the optimal value of (7) is no less than 1/Btimes that of the latter problem, which is the desired result.

For any given set A ⊂ Ω, any element eεΩ, any RB nεN and anynon-negative scalar Δ together with

$\begin{matrix}{{{\max\limits_{\substack{{\chi_{\underset{\_}{e},n}\text{:}\chi_{\underset{\_}{e},n}} \in {\{{0,1}\}} \\ {n \in R_{u}},{\underset{\_}{e} \in {\underset{\_}{B}}_{u,f}}}}{\{ {\underset{\underset{\_}{e} \in {\underset{\_}{B}}_{u,f}}{\Sigma}{\underset{n \in R_{u}}{\Sigma}( {{r_{\underset{\_}{e}}( {{{\underset{\_}{A}}^{(n)}\bigcup\underset{\_}{e}},n} )} - {{\underset{{\underset{\_}{e}}^{\prime} \in {\underset{\_}{A}}^{(n)}}{\Sigma}( {{r_{{\underset{\_}{e}}^{\prime}}( {{\underset{\_}{A}}^{(n)},n} )} - {r_{{\underset{\_}{e}}^{\prime}}( {{{\underset{\_}{A}}^{(n)}\bigcup\underset{\_}{e}},n} )}} )}\psi_{u_{{\underset{\_}{e}}^{\prime}}}}} )}\chi_{\underset{\_}{e},n}} \} \mspace{14mu} {s.t.\mspace{14mu} \underset{\underset{\_}{e} \in {\underset{\_}{B}}_{u,f}}{\Sigma}}\underset{n \in R_{u}}{\Sigma}{r_{\underset{\_}{e}}( {{{\underset{\_}{A}}^{(n)}\bigcup\underset{\_}{e}},n} )}\chi_{\underset{\_}{e},n}}} \leq \Delta_{u}};{{\underset{\underset{\_}{e} \in {\underset{\_}{B}}_{u,f}}{\Sigma}\chi_{\underset{\_}{e},n}} \leq {1{\forall{n \in {R_{u}.}}}}}} & (8)\end{matrix}$

scalars ψ_(u)ε[0,1]∀uε{1, . . . , K}, we define

{tilde over (g)}( e,A,n,Δ)=min{Δ,r _(e) ( A∪e,n)}−Σ _(e′εA) (r _(e′)(A,n)−r _(e′)( A∪e,n))ψ_(u) _(e′)

We note here that {tilde over (g)}(e, A, n, Δ) represents the overallincremental weighted rate gain (or loss) that is obtained by schedulingelement e on RB n given that elements in A are already scheduled on thatRB. Further, in defining this incremental rate we use Δ as a weightedrate margin, i.e., the weighted rate gain obtained for user u _(e)cannot exceed Δ. The purpose of this margin is to enforce the bufferconstraint on user u _(e) with the understanding that user u _(e) hasalready obtained a weighted rate of θ_(u)Q_(u)−Δ as a result of beingscheduled on other RBs. Also, the scalars ψ_(u)ε[0, 1]∀u are discountfactors which again are used to incorporate buffer constraints. Forinstance, the term r _(e′)(A, n)−r _(e′)(A∪e, n) represents the loss inweighted rate of user u _(e′) due to the increased interference arisingfrom scheduling an additional element e. However, this loss is themaximum possible loss which occurs only when the buffer constraint for u_(e′) is inactive. If the buffer constraint for that user is active (asa result of all RBs that have been assigned to u _(e′)) we discount theloss by a factor ψ_(u) _(e′) . We now proceed to offer Algorithm I toapproximately solve (6). Note that this Algorithm adopts an iterativeframework. Notice that in each outer iteration of the algorithm(comprising of all steps within the outer Repeat-Until loop), decisionsmade in the previous iterations are kept fixed. New assignments of RBs,serving TPs and formats to users are made by first using a simple greedyapproach (comprising of all steps within the inner While-Do loop) whileignoring the at-most one format per-user constraint. Then, a balancingstep is done with respect to the formats of a user to ensure that theuser is scheduled with only one format. The obtained result ensures animprovement in system utility while maintaining feasibility. The formatbalancing routine in Step 16 of Algorithm I for a user u:R_(u)≠φ isimplemented as follows. For a given subset B ⊂ Ω and {A ^((n))}, weconsider each format fεF and solve the problem in (8), where B_(u,f)={eεB:u _(e) =u & f _(e) =f_(e)=1}. Notice that (8) is a multiplechoice knapsack problem and hence can be solved for instance via dynamicprogramming or using efficient approximation algorithms. Next, let{circumflex over (f)} denote the format whose associated solutionresults in the highest objective function value for (8). Let S_(u)⊂R_(u) denote the set of RBs that are assigned in the solutionassociated with {circumflex over (f)} and let ê ^((n)), nεS_(u) be thecorresponding elements. Then, we further check if there exists an{circumflex over (n)}εR_(u)\S_(u) and element êεB_(u,{circumflex over (f)}) such that r _(ê) (A^(({circumflex over (n)}))∪ê,{circumflex over (n)})≧Δ_(u)−Σ_(nεS) _(u) r_(ê) _((n)) (A ^((n))∪ê ^((n)),n) and Δ_(u)−Σ_(nεS) _(u) r _(ê) _((n))(A ^((n))∪ê ^((n)),n)>Σ _(e′εA) _(({circumflex over (n)})) (r _(e′)(A^(({circumflex over (n)})),{circumflex over (n)})−r _(e′)(A^(({circumflex over (n)}))∪ê,{circumflex over (n)}))ψ_(u) _(e′) . Incase, these two conditions are not met, we return {ê ^((n))}_(nεS) _(u)as the format balanced solution. Otherwise, we add {circumflex over (n)}to S_(u) and set ê ^(({circumflex over (n)}))=ê before returning {ê^((n))}_(nεS) _(u) as the format balanced solution. Finally, the pruningstep, given a selected subset S, is done as follows.

$\underset{\_}{B} = \{ \begin{matrix}{{\underset{\_}{B}\backslash \{ {{\underset{\_}{e} \in {\underset{\_}{\Omega}\text{:}{\exists{{\underset{\_}{e}}^{\prime} \in \underset{\_}{S}}}}},{u_{\underset{\_}{e}} = u_{{\underset{\_}{e}}^{\prime}}}} \}},{{If}\mspace{14mu} {aggressive}}} \\{{\underset{\_}{B}\backslash \{ {{\underset{\_}{e} \in {\underset{\_}{\Omega}\text{:}{\exists{{\underset{\_}{e}}^{\prime} \in \underset{\_}{S}}}}},{u_{\underset{\_}{e}} = {{{u_{{\underset{\_}{e}}^{\prime}}\&}f_{\underset{\_}{e}}} \neq f_{{\underset{\_}{e}}^{\prime}}}}} \}},{Otherwise}}\end{matrix} $

Notice that the aggressive pruning option subsumes the other option. Theperformance guarantee derived below holds for both pruning options. Wenote that the complexity per-iteration of Algorithm I is O(KJBN²).

We now proceed to derive the approximation guarantee for Algorithm I.Towards this end, specializing the utility to the single user case weassume the following mild inequalities to hold:

r( e′,n)≧G _(f) _(e′) _(,f) _(e) r( e,n),∀ e,e′εΩ:u _(e′) =u _(e) &b_(e′) i=b _(e) ,  (9)

for some constants G_(i,j)ε[0, 1], 1≦i,j≦J with G_(i,i)=1, ∀i. We thendefine the matrix G=[G_(i,j)]εIR₊ ^(J×J). Notice that since we canalways set G_(i,j)=0, (9) itself results in no loss of generality.However G_(i,j)>0 would mean that changing the format from j to iguarantees a weighted rate greater than a fraction G_(i,j) times theoriginal weighted rate for all users, on all RBs and in all instances.We note that for the format example presented before,

${G_{i,j} = \frac{\min \{ {i,j} \}}{\max \{ {i,j} \}}},$

∀i, j.Theorem 2. Algorithm I offers a solution to (6) that has a worst-caseguarantee of at-least

$\frac{\Gamma}{2B},$

i.e., the weighted sum rate value obtained using the solution yielded byit is no less than

$\frac{\Gamma}{2B}$

times that obtained using the optimal solution of (6). Further, Γsatisfies

$\Gamma \geq \frac{1}{J}$

and can be determined via the following LP for any arbitrarily fixed S>0

$\Gamma = {\min\limits_{{x \in {IR}_{+}^{J}},{\theta \in {IR}_{+}}}\{ \theta \}}$$\begin{matrix}{{{{{s.t.\mspace{14mu} 1^{T}}x} = S};{{\sum\limits_{j = 1}^{J}\; {G_{i,j}x_{j}}} \leq {\theta \; S}}},{\forall{i.}}} & (10)\end{matrix}$

Also, when G⁻¹1

0 we have

$\Gamma = {\frac{1}{1^{T}G^{- 1}1}.}$

Proof: Denote the optimal value of (7) by v^(opt). We will consider thefirst outer iteration of Algorithm I (initialized with A ^((n))=φ∀n andB=Ω) and show that the system weighted sum rate value obtained after thefirst iteration itself is at-least a factor Γ/2 times v^(opt). Thisalong with the fact that each iteration of Algorithm I results in animprovement in system utility, together with Proposition I proves thetheorem.

Then, let us define a function h′:{1, . . . , K}×2^(N)→IR₊ as

$\begin{matrix}{{{h^{\prime}( {u,R} )} = {\min \{ {{\nu_{u}Q_{u}},{\underset{n \in R}{\Sigma}{\max\limits_{{\underset{\_}{e} \in {\underset{\_}{\Omega}\text{:}u_{\underset{\_}{e}}}} = u}{r( {\underset{\_}{e},n} )}}}} \}}},} & (11)\end{matrix}$

where uε{1, . . . , K} and R⊂N. Our first observation is that for anyuser u, the set function h′(u,:) is a monotonic submodular set function,i.e., for any R⊂S⊂N and any nεN, we have that 0≦h′(u, R)≦h′(u, S) and

h′(u,R∪{n})−h′(u,R)≧h′(u,S∪{n})−h′(u,S).

Next, consider the following problem,

$\begin{matrix}{{\max\limits_{\underset{{{u \in {\{{1,\ldots \mspace{14mu},K}\}}},{R \subseteq N}}\}}{{\{{{\overset{\sim}{\chi}}_{u,R} \in {\{{0,1}\}}}\}}:}}{\sum\limits_{u \in {\{{1,\ldots \mspace{14mu},K}\}}}{\sum\limits_{R \subseteq N}{{h^{\prime}( {u,R} )}{\overset{\sim}{\chi}}_{u,R}}}}}{{{\sum\limits_{R:{n \in R}}{\sum\limits_{u}{\overset{\sim}{\chi}}_{u,R}}} \leq 1},{\forall{n \in N}}}{{{\sum\limits_{R}{\overset{\sim}{\chi}}_{u,R}} \leq 1},{\forall{u \in {\{ {1,\ldots \mspace{14mu},K} \}.}}}}} & (12)\end{matrix}$

The problem in (12) is a combinatorial auction problem (a.k.a. welfaremaximization problem) with monotonic submodular per-user utilities orvaluations. Notice that since the per-user format constraint is droppedin (12), its optimal value is an upper bound on v^(opt). Moreimportantly, any combinatorial auction problem with monotonic submodularvaluations can be approximately solved (with ½ approximation) via agreedy algorithm. Indeed, the inner While-Do loop implements such agreedy routine as a consequence of which after Step 14 we have thatR_(u)∩R_(u′)=φ∀u≠u′ and

$\begin{matrix}{{\sum\limits_{u = 1}^{K}{h^{\prime}( {u,R_{u}} )}} \geq {v^{opt}/2.}} & (13)\end{matrix}$

Now, let us consider the format balancing routine for a user u: R_(u)≠φ.For such a user u and for each format f let us define

$\begin{matrix}{{{\overset{\sim}{R}( {u,f} )} = {\sum\limits_{{n \in {R_{u}:{\exists{\underset{\_}{\hat{e}}}^{(n)}}}} = {{{{\underset{\_}{A}}^{(n)}\&}{f_{\underset{\_}{\hat{e}}}{(n)}}} = f}}{r( {{\underset{\_}{\hat{e}}}^{(n)},n} )}}},} & (14)\end{matrix}$

with the understanding that {tilde over (R)}(u, f)=0 if such an elementcannot be found on any RB nεR_(u). Note then that the weighted rateobtained for user u (after step 14 of Algorithm I) is equal tomin{θ_(u)Q_(u), Σ_(f=1) ^(J){tilde over (R)}(u, f)} and indeed is equalto h′(u, R_(u)). Then, upon selecting {circumflex over (f)} as per theformat balancing method described above and invoking the inequality in(9), we can ensure that user u gets a rate at-least

$\begin{matrix}{\max\limits_{f:{1 \leq f \leq J}}{\min {\{ {{\vartheta_{u}Q_{u}},{\sum\limits_{f^{\prime} = 1}^{J}{G_{f,f^{\prime}}{\overset{\sim}{R}( {u,f^{\prime}} )}}}} \}.}}} & (15)\end{matrix}$

In addition, since users are assigned non-overlapping RBs, we canconclude that the worst-case approximation guarantee of the formatbalancing routine for the given instance is at-least

$\begin{matrix}{\min\limits_{u}\frac{\max_{f:{1 \leq f \leq J}}{\min \{ {{\vartheta_{u}Q_{u}},{\sum\limits_{f^{\prime} = 1}^{J}{G_{f,f^{\prime}}{\overset{\sim}{R}( {u,f^{\prime}} )}}}} \}}}{\min \{ {{\vartheta_{u}Q_{u}},{\sum\limits_{f = 1}^{J}{\overset{\sim}{R}( {u,f} )}}} \}}} & \;\end{matrix}$

where the outer minimization is over all users u: R≠φ. Then, theworst-case approximation guarantee over all instances can be lowerbounded by Γ, which is the solution to the problem

$\begin{matrix}{\min\limits_{x \in {IR}_{+}^{J}}\frac{\max_{f:{1 \leq f \leq J}}{\min \{ {{\vartheta_{u}Q_{u}},{\sum\limits_{f^{\prime} = 1}^{J}{G_{f,f^{\prime}}x_{f^{\prime}}}}} \}}}{\min \{ {{\vartheta_{u}Q_{u}},{\sum\limits_{f = 1}^{J}x_{f}}} \}}} & (16)\end{matrix}$

Clearly, since Gε[0,1]^(J×J)& G_(f,f)=1, ∀f we see that the minimalvalue in (16) can be no less than

$\frac{1}{J}.$

The remaining parts of the theorem follow upon invoking Proposition 2proved in Appendix A.

In Tables I and II we provide evaluation results for Algorithm I, wherethe evaluations were done on a fully calibrated system simulator whichemulates a HetNet (scenario 4b). In particular, a HetNet with 19cell-sites (with wraparound) and 3 sectors per cell-site is emulated,where each sector represents a cluster comprising of 5 TPs—one Macrobase-station and 4 low power radio heads—each with 4 transmit antennas.Each sector serves an average of 10 users (each with 2 receive antennas)and a full buffer model is assumed. In Table I we assume that each useremploys a simple receiver without inter-cell interference (ICI)rejection capabilities, whereas in Table II a more robust MMSE-IRCreceiver is employed. In each case we suppose that all users are eitherDPS users or that all users are CS/CB users. Also, the feedback obtainedfrom each user was further refilled using the ACK/NACK feedback and wehasten to add that only the feedback provisioned has been employed. Fromthe tables, where the percentage gains are over the baseline singlepoint scheduling, we see

[Algorithm I: Iterative Algorithm for CS/CB or DPS: Finite Buffers]  1)Initialize 

 = Ω, {

, {ψ_(u) = 1, Δ_(u) = Q_(u)}∀ u and Iter = 0.  2) REPEAT  3) Set 

 = 

 , Iter = Iter + 1, done = false and

 = φ, Θ_(u) = Δ_(u) ∀u.  4) WHILE (done = false) DO  5) Determine  $\mspace{11mu} \{ {g( {\underset{\_}{e},,n,\Theta_{u_{\underset{\_}{e}}}} )} \}$(17) and let {circumflex over (v)}, {circumflex over (n)} and

 denote the optimal value and the corresponding RB and element,respectively.  6) IF {circumflex over (v)} > 0 THEN  7)$ {{Update}\mspace{14mu} }arrow{\mspace{11mu}\bigcup\; \hat{n}} ,{ Sarrow{{S \smallsetminus \hat{n}}\mspace{14mu} {and}\mspace{11mu} \Theta_{u_{\underset{\_}{ê}}}}  = ( {\Theta_{u_{\underset{\_}{ê}}} - {r_{\underset{\_}{ê}}( {{\;\bigcup\; \underset{\_}{ê}},\hat{n}} )}} )^{+}}$ 8) ELSE  9) done = true 10) END IF 11) IF 

 = φ THEN 12) done = true 13) END IF 14) END WHILE 15) FOR each user u :

 ≠ φ DO 16) Determine assigned RB set

 and corresponding elements

, n ∈ 

 using the format balancing routine 17)$ {{Update}\; }\;arrow\; {\;\bigcup\; {\underset{\_}{ê}}^{(n)}} ,{\forall{n \in S_{u}}}$18) END FOR 19) FOR each user u DO 20)${{Update}\mspace{14mu} \Delta_{u}} = {{( {{\vartheta_{u}Q_{u}} - {\mspace{11mu} {r_{\underset{\_}{e}}( {\;,n} )}}} )^{+}{and}\mspace{14mu} \psi_{u}} = \quad}$21) END FOR 22) Prune    using  the  set   23) UNTIL 

  = 

 or Iter = IterMax 24) Output {

}, n ∈ 

that significant gains in the 5% spectral efficiency (SE) can beobtained via joint scheduling. This in turn would ensure improved userexperience irrespective of its location, while retaining most of thecell-splitting average SE gains that have been captured by the baseline.Also, the gains are better when simpler receivers are used since thennetwork aided coordinated transmission is more needed to manage ICI.

III. Conclusions

We considered resource allocation in HetNets. Our detailed analysis andsystem evaluations show that by exploiting all the available feedback ina certain manner and by using a well-designed algorithm, significantgains can indeed be realized over realistic HetNets.

APPENDIX A. Appendix: Proposition 2 and Proof

Proposition 2. For any matrix Gε[0, 1]^(J×J), where J≧1 is a fixedpositive integer, and any Δ>0, the solution to

$\begin{matrix}{\min\limits_{x \in {IR}_{+}^{J}}\frac{\min \{ {\Delta,{\max_{i:{1 \leq i \leq J}}{\sum\limits_{j = 1}^{J}{G_{i,j}x_{j}}}}} \}}{\min \{ {\Delta \;,{\sum\limits_{j = 1}^{J}x_{j}}} \}}} & (18)\end{matrix}$

can be found by solving the following linear program for any constantS>0,

$\begin{matrix}{{\min\limits_{{x \in {IR}_{+}^{J}},{\theta \in {IR}_{+}}}\{ \theta \}}{{{s.t.\mspace{14mu} 1^{T}}x} = S}{{{\sum\limits_{j = 1}^{J}{G_{i,j}x_{j}}} \leq {\theta \; S}},{\forall{i.}}}} & (19)\end{matrix}$

Furthermore, in the special case of G⁻¹1

0, the solution to (18) can be obtained in closed form as

$\frac{1}{1^{T}G^{- 1}1}.$

Proof: Denote the optimal value of (18) by Â. Then, using any constant0<S≦Δ, it can be upper bounded as

$\begin{matrix}{\hat{A} \leq {\min\limits_{{x \in {{IR}_{+}^{J}:{1^{T}x}}} = S}\{ {\frac{1}{S}{\max\limits_{i:{1 \leq i \leq J}}{\sum\limits_{j = 1}^{J}{G_{i,j}x_{j}}}}} \}}} & (20)\end{matrix}$

Furthermore, we see that

$\begin{matrix}{\hat{A} \geq {\min\limits_{x \in {IR}_{+}^{J}}\frac{\max_{i:{1 \leq i \leq J}}{\sum\limits_{j = 1}^{J}{G_{i,j}x_{j}}}}{\sum\limits_{j = 1}^{J}x_{j}}}} & (21)\end{matrix}$

Now, suppose {circumflex over (x)} is an optimal solution to the RHS of(21) with max_(i:1≦i≦J)Σ_(j=1) ^(J)G_(i,j){circumflex over(x)}_(j)={circumflex over (α)} and 1^(T){circumflex over (x)}=Ŝ so that

$\frac{\hat{\alpha}}{\hat{S}}$

is the optimal value for the RHS of (21). Then, consider the convexminimization problem in the RHS of (20) for any constant S>0. Clearly{tilde over (x)}=γ{circumflex over (x)}, where

${\gamma = \frac{S}{S}},$

is feasible for the RHS of (20) and yields a value

$\frac{\hat{\alpha}}{\hat{S}}.$

This implies that the optimal value of the RHS of (20) is no greaterthan

$\frac{\hat{\alpha}}{\hat{S}}.$

However, an optimal value of the RHS of (20) which is strictly less than

$\frac{\hat{\alpha}}{\hat{S}}$

would result in a contradiction since it would imply that the optimalvalue of the RHS of (21) is also strictly less than

$\frac{\hat{\alpha}}{\hat{S}}.$

Consequently, for arbitrarily fixed S>0 the optimal value of the RHS of(20) is identical to that of the RHS of (21), which implies that thisvalue is identical to Â. Then, (20) can be re-formulated as in (19).Clearly since the constraints and objective in (19) are affine, it is aconvex optimization problem which implies that any solution to the K.K.Tconditions is also globally optimal. Next, the K.K.T conditions for (19)are given by

$\begin{matrix}{{{{1^{T}x} = S};{x \in {IR}_{+}^{J}};{{\theta \; S} \geq {\sum\limits_{j = 1}^{J}{G_{i,j}x_{j}{\forall i}}}}}{{{\beta^{T}1} = \frac{1}{S}};{{\beta^{T}G} = {\lambda^{T} + {\delta \; 1^{T}}}};{\beta \in {IR}_{+}^{J}};{\lambda \in {IR}_{+}^{J}}}{{{{\lambda \odot x} = 0};{{\beta \odot ( {{Gx} - {\theta \; S\; 1}} )} = 0};{\delta \in {IR}}},}} & (22)\end{matrix}$

TABLE I SPECTRAL EFFICIENCY (BPS/HZ) WITH SIMPLE RECEIVER. Schedulingscheme DPS CS/CB Baseline cell average 2.4006 (−1.20%) 2.4617 (1.32%)2.4297 5% cell-edge 0.0962 (19.35%) 0.0856 (6.20%) 0.0806

TABLE II SPECTRAL EFFICIENCY (BPS/HZ) WITH MMSE-IRC RECEIVER. Schedulingscheme DPS CS/CB Baseline cell average 2.7168 (−3.01%) 2.7656 (−1.27%)2.8811 5% cell-edge 0.1289 (21.83%) 0.1087 (2.74%)  0.1058where ⊙ denotes the Hadamard product. Next, suppose that G⁻¹1≧0. Then,consider a particular choice

$\begin{matrix}{{{x = {( {\theta \; S} )G^{- 1}1}};{\theta = \frac{1}{1^{T}G^{- 1}1}}}{{\delta = \frac{1}{S\; 1^{T}G^{- 1}1}};{\lambda = 0};{\beta^{T} = {\delta \; 1^{T}{G^{- 1}.}}}}} & (23)\end{matrix}$

It can be verified that the choice in (23) satisfies all the K.K.T.conditions in (22) and hence must yield a global optima for (19) andthus the optimal value for (18). This optimal value can be verified tobe

$\frac{1}{1^{T}G^{- 1}1}.$

Further System Details C 1 Introduction

It has been agreed that three CoMP schemes, namely, joint transmission(JT), coordinated scheduling and beamforming (CS/CB), and dynamic pointselection (DPS), will be supported in Rel-11 [6]. In CoMP CS/CB, thedata will be transmitted through the transmission point (TP) of theserving cell, same as the case in conventional single cell (withoutCoMP) systems. Therefore, there is no issue on the PDSCH mapping forCoMP CS/CB. However, in CoMP JT and DPS, the TP or TPs other than thatof the serving cell might be involved in the data transmission. In thiscase some problems arise due to different signalling structures onPhysical Downlink Shared Channel (PDSCH) resource element (RE) mapping,e.g., the CRS/PDSCH collision due to different frequency shifts for theCRS RE positions corresponding to different TPs, and the PDSCH startpoint due to different sizes of the PDCCH regions for different TPs.These issues have been realized and discussed in the CoMP study itemstage itself, and have been included in the CoMP WI [6][7].

In RAN1#69, the way to solve the PDSCH RE mapping issues in CoMP hasbeen discussed and additional downlink control signalling might beneeded to solve these issues. The following has been agreed in RAN1#69meeting:

-   -   Provide signalling to indicate the CRS position of at least        onecell from which PDSCH transmission may occur        -   Signalling identifies at least the frequency shift        -   FFS for number of CRS antenna ports        -   FFS for MBSFN subframes    -   If the signalling is transmitted, PDSCH follows the Rel-10        rate-matching around the indicated CRS of a single cell;        otherwise, the UE assumes the CRS positions of the serving cell        -   FFS until RAN1#70 whether the signalling can also indicate            up to 3 cells around whose combined CRS patterns the PDSCH            is rate-matched.

Several alternatives have been introduced in [8] on the DL controlsignal for CoMP PDSCH mapping, either semi-statically or dynamically. Weprovide some detailed signal designs for different alternatives anddiscussions on these schemes.

2 PDSCH Mapping Operations in CoMP

2.1 PDSCH Mapping Issues in CoMP

In CoMP JT and DPS transmissions, since the transmission points otherthan the serving cell are involved in the actual data transmissions, theUE does not have the knowledge of the exact PDSCH RE mapping unless acertain assumption or additional DL control signal is specified. ThePDSCH mapping for CoMP JT and DPS has the following issues.

-   -   The CRS/PDSCH collision or the CRS positions of the transmission        points for PDSCH transmissions.    -   The starting point (OFDM symbol) of the PDSCH due to different        sizes of PDCCH regions.    -   The information of MBSFN subframes.

The details of these issues have been discussed and several alternativesolutions have been provided in [8]. We further discuss the PDSCH REmapping solutions and their necessary DL control signalling.

2.2 PDSCH RE Mapping Solutions in CoMP

The default PDSCH mapping approach for CoMP JT and DPS is that the PDSCHmapping always aligns with the mapping of the serving cell including thePDSCH start point and the assumption on the CRS RE positions. Thisdefault approach does not need to introduce additional DL signalling,and thus has minimum standard impact. However, due to mismatched PDCCHregions and CRS/PDSCH collisions, some RE resources can be wasted orexperience strong interference from CRS signals of other cells. Thussuch default approach can incur large CoMP performance degradation onthe spectral efficiency.

Some potential solutions to solve the CRS/PDSCH collision issue in CoMPare summarized in [4], e.g. not using any OFDM symbols that contain CRSREs or only using MBSFN subframe for CoMP JT or DPS transmissions wherethere is no CRS, as also suggested in [9]. However, these approaches areeither not spectrally efficient or are restricted to some specificsettings. It is argued in [9] that the approach of using the MBSFN isstill spectral efficient in the sense that the CoMP is primarily usefulin the high load case. However, it is known that CoMP JT provides largergains on the cell edge when the system load is low. Some companies alsosuggested that eNB aligns the CRS positions for the TPs in the CoMPcoordinate set by configuring the same CRS frequency shift. However,this approach, if it is implementable at eNB, increases the eNBcomplexity significantly. On the other hand, it does not solve the issueif the two TPs have different number of CRS ports.

Several alternatives have been provided in [8] to solve the PDSCHmapping issues. The first approach to address the CRS/PDSCH collisionissue is based on PDSCH muting, i.e., not transmitting the data symbolon the REs that are collided with the CRS REs from other TPs. The PDSCHmapping information with PDSCH RE muting may then be signalled to theCoMP UE. If we send exact PDSCH mapping to the CoMP UE dynamically, thePDSCH RE muting may not be needed for the CoMP DPS. However, dynamicallytransmitting the exact PDSCH mapping requires a large signallingoverhead. Therefore, the PDSCH muting based on the CoMP measurement setseems a promising alternative solution if the dynamic signalling cannotbe accommodated. Here all the PDSCH REs that collide with the CRS REsfrom any other TP with the corresponding CSI-RS resource in the CoMPmeasurement set are muted for data transmission. Since the measurementset is semi-statically configured, the PDSCH mapping with muting can besignalled to the UE semi-statically. Also it has been agreed that themaximum size of CoMP measurement size is 3. Thus, PDSCH muting based onthe measurement set will not degrade the spectral efficiency performancemuch.

Alternative 1: For CoMP JT or DPS, the network semi-statically informsthe CoMP UE the union of the CRS RE patterns for the TPs or CSI-RSresources in the CoMP measurement set of the UE, which are excluded fromthe data transmissions in PDSCH to that UE.

To signal the CoMP UE the union of the CRS RE patterns, we cansemi-statically signal the frequency shift, v, and number of port ofCRS, p, for M TPs in the measurement set, i.e., (v_(m), p_(m)), m=1, . .. , M. The information of MBSFN subframes from each TP in themeasurement set can also be signalled to the CoMP UE semi-statically.

To also accommodate the CoMP CS/CB transmissions which the PDSCH mappingis configured according to that for the serving cell, we then use oneadditional bit along with the signals of the CRS RE patterns to the UEto indicate that the PDSCH RE mapping is according to the serving cellor around all CRS positions in the measurement set, as shown in Table 1.Note that the union of the CRS REs is the union of the existed CRS RE inthat subframe. If the MBSFN subframe configurations are signalled to theCoMP UE, the union of CRS REs do not include the CRS RE pattern for theTP if it is on its MBSFN subframe.

TABLE 1 CoMP PDSCH RE mapping indication for alternative 1. CoMP PDSCHMapping Indicator CoMP PDSCH RE Mapping 0 Align to the serving cell(TP-1) 1 RE mapping on a subframe excluding the union of CRS REs of TPsin the measurement set on that subframe.

A question might be raised whether this semi-static approach is betterthan the default approach. In the default approach, eNB configures PDSCHRE mapping for any transmitting TP as that for the serving cell. In DPS,when a TP other than the serving TP in the measurement set istransmitting, the PDSCH on the CRS positions for this TP will not beused for data transmission. Since the UE assumes the serving cell PDSCHmapping, it would still try to decode the data on these CRS positionswhich actually do not carry any data information, which are called dirtydata/bits. A simple simulation is performed to evaluate the performanceof these scenarios. A length-576 information bits is encoded using theLTE turbo code with rate-½. We assume there are total 5% coded bitsaffected by CRS/PDSCH collisions. We compare the performance of thisrate-½ codes in AWGN channel with puncturing 5% coded bits (PDSCHmuting), 5% dirty received data (purely noise), and 2.5% puncturing plus2.5% dirty data. The results are shown in FIG. 9. We can see with 5%dirty bits, there is significant performance degradation. Even with halfof dirty bits on the collided RE positions, there is still an observableperformance loss compared to RE muting.

To improve the performance gain over the default approach, we mayconsider the following semi-static approach.

Alternative 2: For CoMP JT or DPS, the network semi-statically informs aCoMP UE the CRS information for each TP in the CoMP measurement set ofthat UE, and the PDSCH mapping that the network will follow to servethat UE.

In this approach, we can first semi-statically signal the UE thefrequency shift of the CRS and number of CRS ports for each TP in themeasurement set as that in Alternative 1. Again the CRS information istagged with the TP index. We then signal the UE an indicator for the TPindex which the eNB will configure the PDSCH mapping according to. Sincethere are at most 3 CRS-RS resources in a CoMP measurement set, atwo-bit indicator is enough to carry the information. We can alsoinclude the option of the PDSCH mapping around of all the CRS REs in asubframe as shown in Table 2. This approach is particularly useful whenthe cell range expansion is applied to some UEs in the HetNet scenario,in which the network may always configure the macro cell eNB for the DLdata transmission.

TABLE 2 CoMP PDSCH RE mapping indication for alternative 2. CoMP PDSCHMapping Indicator CoMP PDSCH RE Mapping 00 PDSCH mapping align to theserving cell (TP-1 in the measurement set) 01 PDSCH mapping align toTP-2 in the measurement set 10 PDSCH mapping align to TP-3 in themeasurement set 11 RE mapping excluding the union of CRS REs in themeasurement set in a subframe.

Note that instead of the CRS frequency shift and the number of CRSports, we may signal the UE the list of cell IDs of the TP in themeasurement set and the associated number of CRS ports. If the cell IDsin the measurement set are signalled to the CoMP UE, the interferencecancellation can be implemented since the UE is able to decode all theCRS signals in its CoMP measurement set. Also note that with thediscussions for FeICIC, it has been agreed that the list of the strongCRS interference will be signalled to the UE so that UE may perform theinterference cancellation. Since most probably, the TPs other than theserving TP in the measurement set are included in this list, it is thenpossible to reuse this list for the CoMP PDSCH mapping to reduce thesignal overhead.

The network can also semi-statically inform the UE the PDSCH startpoint. However for DPS, if there is a mismatch between the PDSCH startpoints for the TPs in the CoMP measurement set, it will cause spectralefficiency loss. We now consider the following hybrid approach to conveythe PDSCH mapping information dynamically.

Alternative 3: For CoMP JT or DPS, the network semi-statically informs aCoMP UE the CRS information and PDSCH start point for each TP in theCoMP measurement set of that UE in some order. The network then informsthe UE dynamically the PDSCH start point and CRS pattern that the PDSCHmapping will follow by conveying the indices corresponding to them.

With this approach, the network first semi-statically signals the UE theCRS information for each TP in the measurement set as in Alternative 1or Alternative 2, as well as the PDSCH starting point for each TP ifPDCCH region changes semi-statically. Then the network dynamicallysignal the index of the TP that the PDSCH mapping follows including thestarting point. Such dynamic signal can be specified in DCI withintroducing an additional signal field. The signal is similar to that inTable 2 except that the index for the muting on the union of CRS REs isnot necessary. If the PDSCH start points are configured dynamically oneach TP in the measurement set. It may be better also dynamically signalthe PDSCH start point.

For CoMP JT, more than one TP will be involved in the transmission. Forthis case, in the hybrid approach with dynamical signalling available,instead of mapping avoiding the CRS positions for all TPs in the cell,we propose the PDSCH RE mapping sequentially occupying all CRS REs, justthat on the collided CRS REs, single TP or the subset of TPs (for 3TPJT) might be assigned for the signal transmissions if they are notscheduled all on MBSFN subframe. We then have the following alternativescheme.

Alternative 4: For CoMP JT or DPS, the network semi-statically informs aCoMP UE the CRS information for each TP in the CoMP measurement set ofthat UE in some order. The network then informs the UE dynamically theCRS pattern that the PDSCH mapping will follow by conveying the indicescorresponding to them or indicating the UE the PDSCH mapping occupyingall the CRS RE positions (assuming no CRS).

The dynamic signal for mapping indicator is then given in Table 3. Whenthe PDSCH mapping indicator is set to be 11, the PDSCH starting pointcan be set with assuming the minimum or maximum size of PDCCH regions(or PDCCH OFDM symbols) of the TPs in the measurement set, which aresemi-statically informed to the UE.

TABLE 3 CoMP PDSCH RE mapping indication for alternative 3, 4. CoMPPDSCH Mapping Indicator CoMP PDSCH RE Mapping 00 PDSCH mapping align tothe serving cell (TP-1 in the measurement set) 01 PDSCH mapping align toTP-2 in the measurement set 10 PDSCH mapping align to TP-3 in themeasurement set 11 (Alt-4) PDSCH RE mapping by occupying all CRS REs inthe measurement set (assuming no CRS).

Note that the first three cases (00, 01, 10) in Table 3 can also beapplied to the JT with the corresponding indicated TP in non-MBSFNsubframe and other TPs in their MBSFN subframe, which can also beindicated with 11. No CRS JT is done in MBSFN case or it might bepossible to realize sometimes using eNB compensation for partial JT. Forthe last case (11) in Table 3, i.e., assuming no CRS, JT can be done inMBSFN case. But it might be possible to realize sometimes using eNBcompensation for partial JT, i.e., transmission over single TP or thesubset of TPs (for 3TP JT). Also the PDSCH RE mapping assuming no CRScan be included in as a pattern with number of CRS port being 0.

The UE may estimate the channel with the precoded demodulation referencesignal (DMRS), then use such estimated channel to demodulate/detect thedata symbol for all data symbols in the resource block or the resourcegroup. If we transmit the data symbol on a subset of TPs, with the sameprecodings as that for the normal JT using all configured JT TPs, therewould be channel mismatch which may degrad demodulation performance. Toperform partial JT on some REs with and make the UE see the similarcombined channel for demodulation as the normal JT on other REs, we mayconsider to use different precoding on the subset of TPs in the partialJT. We now consider a case of the partial JT for a configured 2TP JT.The precoding for the transmission on the single TP on the collided REcan be obtained as follows. Assume U₁ and U₂ are two precoding matricesemployed on 2 TPs in the JT. The received signal seen at the UE can bewritten as

y=H ₁ U ₁ x+H ₂ U ₂ x+n.

For partial JT with data being transmitted on 1-TP, without loss ofgenerality, assuming TP-2, we have

{tilde over (y)}=H ₂ Ux+n

To ensure that the UE sees the same combined channel, we then let

U=H ₂ ⁻¹ H ₁ U ₁ +U ₂,

where H₂ ⁻¹ denotes the right inverse of H₂, i.e., H₂ ⁻¹=H₂ ^(H) (H₂H₂^(H))⁻¹. Denote the

$D_{i}^{\frac{1}{2}} = {{diag}( {\sqrt{\gamma_{i\; 1}},\ldots,\sqrt{\gamma_{ir}}} )}$

where γ_(ij) as the SINR feedback (e.g. in a quantized form CQI) for thei-th TP(CSI-RS resource) and the j-th layer, accompanied with thepreferred precoding G_(i) of rank r. We assume common rank on 2 TPs forthe JT. The network can approximate the channel as

${\overset{\sim}{H}}_{i} = {D_{i}^{\frac{1}{2}}{G_{i}^{H}.}}$

We then have (H₂H₂ ^(H))⁻¹≈D₂ ⁻¹, and then

U=U ₂ +G ₂ D ₂ ^(−1/2) D ₁ ^(1/2) G ₁ ^(H) U ₁.  (1)

The above precoding scheme can be easily extended to the general case,i.e., the partial JT using a subset of TPs, say m TPs for the normal JTwith M_(JT) TPs, m<M_(JT.)

The normalized U can then be employed as the precoding matrix for TP-2.Since U is normalized/scaled, the eNB can decide if this scaling resultin an acceptable performance or not.

To semi-statically signal the CRS pattern for each TP in the UEmeasurement set using the number of CRS ports and its frequency shift(instead of cell ID), the 4-bit indices for CRS patterns are summarizedin Table 4. With this setting, the MSB b₃ of the CRS pattern indexdefines if the number of CRS port M=1 (b₃=0) or M>1 (b₃=1). If b₃=0, therest three bits (b₂b₁b₀) indicate the frequency shift. If b₃=1, the2^(nd) MSB b₂ is used to differentiate M=2 (b₂=0) or M=4 (b₂=1), thenthe rest two bits (b₁b₀) indicate the frequency shift (binaryrepresentation). We can see that with the indexing in Table 4, we alwayshave several bits in the index (3 bits for 1 CRS port, 2 bits for 2 or 4CRS ports) explicitly mapped to the frequency shift of CRS. If the caseof no CRS (number of CRS port=0) is also needed to be semi-staticallysignalled as one of CRS patterns, we can use one of the reserved index,e.g., b₃b₂b₁b₀=1111, to convey this information.

TABLE 4 CRS pattern indexes. CRS pattern index Number of Frequency shift(b₃b₂b₁b₀) CRS ports of CRS 0000 1 0 0001 1 1 0010 1 2 0011 1 3 0100 1 40101 1 5 0110 Reserved Reserved 0111 Reserved Reserved 1000 2 0 1001 2 11010 2 2 1011 Reserved Reserved 1100 4 0 1101 4 1 1110 4 2 1111 ReservedReserved

Based on above discussions, for the semi-static approaches,Alternative-2 seems better as one additional bit signal overhead is notcritical for the semi-static signalling. Therefore for the semi-staticapproach, we propose

Proposal 1: For PDSCH mapping in CoMP, the network semi-staticallyinforms a CoMP UE the CRS information of each TP in its CoMP measurementset, and either an indicator of the PDSCH mapping of the TP from theCoMP measurement set that the network will follow to serve that UE orthe PDSCH mapping which excludes the union of the CRS REs of all the TPsin the CoMP measurement set.

If some dynamic signalling (e.g. 2 bits in DCI) can be introduced tohandle PDSCH mapping issues, Alternative-4 is preferable. Therefore, wepropose the following for the hybrid approach with dynamic signallinggiven in Table 3.

Proposal 2: For PDSCH mapping in CoMP, the network semi-staticallyinforms a CoMP UE the CRS information of each TP in its CoMP measurementset. The network then informs the UE dynamically the CRS pattern thatthe PDSCH mapping will follow by conveying an index identifying it or byindicating to the UE that the PDSCH mapping will occupy all the CRS REpositions.

The presented precoding scheme in (1) can be an efficient implementationfor partial JT if we transmit some data symbols from a subset of JT TPson some REs in a JT CoMP transmission.

3 Conclusion

In this document, the PDSCH mapping issues for CoMP JT and DPS have beendiscussed. We consider the following two alternatives (one withsemi-static signaling only and one with dynamic signaling) for the PDSCHmapping in CoMP:

Proposal 1: For PDSCH mapping in CoMP, the network semi-staticallyinforms a CoMP UE the CRS information of each TP in its CoMP measurementset, and either an indicator of the PDSCH mapping of the TP from theCoMP measurement set that the network will follow to serve that UE orthe PDSCH mapping which excludes the union of the CRS REs of all the TPsin the CoMP measurement set.

Proposal 2: For PDSCH mapping in CoMP, the network semi-staticallyinforms a CoMP UE the CRS information of each TP in its CoMP measurementset. The network then informs the UE dynamically the CRS pattern thatthe PDSCH mapping will follow by conveying an index identifying it or byindicating to the UE that the PDSCH mapping will occupy all the CRS REpositions.

The presented precoding scheme in (1) can be an efficient implementationfor partial JT if we transmit some data symbols from a subset of JT TPson some REs in a JT CoMP transmission. And also the proposed the CRSpattern indexing in Table 4 has an advantage that have several bits inthe index (3 bits for 1 CRS port, 2 bits for 2 or 4 CRS ports)explicitly mapped to the frequency shift of CRS.

Further System Details D 1 Introduction

It has been agreed that three CoMP schemes, namely, joint transmission(JT), coordinated scheduling and beamforming (CS/CB), and dynamic pointselection (DPS), will be supported in Rel-11[6]. In CoMP CS/CB, the datawill be transmitted through the transmission point (TP) of the servingcell, same as the case in conventional single cell (without CoMP)systems. Therefore, there is no issue on the PDSCH mapping for CoMPCS/CB. However, in CoMP JT and DPS, the TP or TPs other than that of theserving cell might be involved in the data transmission. In this casesome problems arise due to different signalling structures on PDSCH REmapping, e.g., the CRS/PDSCH collision due to different frequency shiftsfor the CRS RE positions corresponding to different TPs, and the PDSCHstart point due to different sizes of the PDCCH regions for differentTPs. These issues have been realized and discussed in the CoMP studyitem stage itself, and have been included in the CoMP WI [6][7].

In RAN1#69, the way to solve the PDSCH RE mapping issues in CoMP hasbeen discussed and additional downlink control signalling might beneeded to solve these issues. The following has been agreed in RAN1#69meeting:

-   -   Provide signalling to indicate the CRS position of at least        onecell from which PDSCH transmission may occur        -   Signalling identifies at least the frequency shift        -   FFS for number of CRS antenna ports        -   FFS for MBSFN subframes    -   If the signalling is transmitted, PDSCH follows the Rel-10        rate-matching around the indicated CRS of a single cell;        otherwise, the UE assumes the CRS positions of the serving cell        -   FFS until RAN1#70 whether the signalling can also indicate            up to 3 cells around whose combined CRS patterns the PDSCH            is rate-matched.

We further discuss the candidate approaches and provide some detailedsignal designs.

2 Discussions

2.1 PDSCH Mapping Issues in CoMP

In CoMP JT and DPS transmissions, since the transmission points otherthan the serving cell are involved in the actual data transmissions, theUE does not have the knowledge of the exact PDSCH RE mapping unless acertain assumption or additional DL control signal is specified. ThePDSCH mapping for CoMP JT and DPS has the following issues.

-   -   The CRS/PDSCH collision or the CRS positions of the transmission        points for PDSCH transmissions.    -   The starting point (OFDM symbol) of the PDSCH due to different        sizes of PDCCH regions.    -   The information of MBSFN subframes.

2.2 PDSCH RE Mapping Solutions in CoMP

Before discussing the above dynamic signalling alternatives, we firstrecap the possible semi-static approaches. If dynamic approaches do notprovide significant performance gain with additional signal overhead,the semi-static approaches can be a tradeoff solution. For semi-staticapproach, we consider the PDSCH muting over the CRS collided REs, i.e.,all the PDSCH REs that collide with the CRS REs from any other TP withthe corresponding CSI-RS resource in the CoMP measurement set are mutedfor data transmission. Since the measurement set is semi-staticallyconfigured, the PDSCH mapping with muting can be signalled to the UEsemi-statically. Also it has been agreed that the maximum size of CoMPmeasurement size is 3. Thus, PDSCH muting based on the measurement setwill not degrade the spectral efficiency performance much.

Alternative 1: For CoMP JT or DPS, the network semi-statically informsthe CoMP UE the union of the CRS RE patterns for the TPs or CSI-RSresources in the CoMP measurement set of the UE, which are excluded fromthe data transmissions in PDSCH to that UE.

To signal the CoMP UE the union of the CRS RE patterns, we cansemi-statically signal the frequency shift, v, and number of port ofCRS, p, for M TPs in the measurement set, i.e., (v_(m), p_(m)), m=1, . .. , M. The information of MBSFN subframes from each TP in themeasurement set can also be signalled to the CoMP UE semi-statically.

To also accommodate the CoMP CS/CB transmissions which the PDSCH mappingis configured according to that for the serving cell, we then use oneadditional bit along with the signals of the CRS RE patterns to the UEto indicate that the PDSCH RE mapping is according to the serving cellor around all CRS positions in the measurement set, as shown in Table 1.Note that the union of the CRS REs is the union of the existed CRS RE inthat subframe. If the MBSFN subframe configurations are signalled to theCoMP UE, the union of CRS REs do not include the CRS RE pattern for theTP if it is on its MBSFN subframe.

TABLE 1 CoMP PDSCH RE mapping indication for alternative 1. CoMP PDSCHMapping Indicator CoMP PDSCH RE Mapping 0 Align to the serving cell(TP-1) 1 RE mapping on a subframe excluding the union of CRS REs of TPsin the measurement set on that subframe.

To improve the performance gain over the default approach, we mayconsider the following semi-static approach.

Alternative 2: For CoMP JT or DPS, the network semi-statically informs aCoMP UE the CRS information for each TP in the CoMP measurement set ofthat UE, and the PDSCH mapping that the network will follow to servethat UE.

In this approach, we can first semi-statically signal the UE thefrequency shift of the CRS and number of CRS ports for each TP in themeasurement set as that in Alternative 1. Again the CRS information istagged with the TP index. We then signal the UE an indicator for the TPindex which the eNB will configure the PDSCH mapping according to. Sincethere are at most 3 CRS-RS resources in a CoMP measurement set, atwo-bit indicator is enough to carry the information. We can alsoinclude the option of the PDSCH mapping around of all the CRS REs in asubframe as shown in Table 2. This approach is particularly useful whenthe cell range expansion is applied to some UEs in the HetNet scenario,in which the network may always configure the macro cell eNB for the DLdata transmission.

TABLE 2 CoMP PDSCH RE mapping indication for alternative 2. CoMP PDSCHMapping Indicator CoMP PDSCH RE Mapping 00 PDSCH mapping align to theserving cell (TP-1 in the measurement set) 01 PDSCH mapping align toTP-2 in the measurement set 10 PDSCH mapping align to TP-3 in themeasurement set 11 RE mapping excluding the union of CRS REs in themeasurement set in a subframe.

Note that instead of the CRS frequency shift and the number of CRSports, we may signal the UE the list of cell IDs of the TP in themeasurement set and the associated number of CRS ports. If the cell IDsin the measurement set are signalled to the CoMP UE, the interferencecancellation can be implemented since the UE is able to decode all theCRS signals in its CoMP measurement set. Also note that with thediscussions for FeICIC, it has been agreed that the list of the strongCRS interference will be signalled to the UE so that UE may perform theinterference cancellation. Since most probably, the TPs other than theserving TP in the measurement set are included in this list, it is thenpossible to reuse this list for the CoMP PDSCH mapping to reduce thesignal overhead.

The network can also semi-statically inform the UE the PDSCH startpoint. However for DPS, if there is a mismatch between the PDSCH startpoints for the TPs in the CoMP measurement set, it will cause spectralefficiency loss.

In the above semi-static approach, for the fourth state, the data is nottransmitted on the union of CRS REs in the measurement set. If moreindication bits can be assigned, we can include more combinations interm of union of CRS REs in the CoMP measurement set. For example, withthe 3-bit indication, i.e., 8 states, the union of CRS REs for anycombination of TPs in the measurement set (with maximum size 3) can beaccommodated. The PDSCH RE mapping is then followed by excluding theunion of CRS RE pattern which is conveyed to the UE by the 3-bitindicator.

This semi-static approach can be further extended to the general casewhen the information of strong interfering CRS outside the CoMP clusteris available to UE as a feature of FeICIC. We know that some UEs arelocated on the boundary of the CoMP cluster. Thus the stronginterference to those UEs may come from some TPs outside CoMP cluster,while the TPs in a UE's CoMP measurement set may not have comparableinterference strength. Although based on the interfering CRS list, theUE can perform interference cancellation to remove the CRS interferenceto improve the decoding performance, additional complexity is incurredto the UE for including such feature. To reduce the UE complexity, onesolution is not to transmit the data over the RE that is interfered bythe TP even outside the CoMPs. Then UE does not need to do theinterference cancellation or have such feature. Thus the PDSCH mappingcan avoid the union of CRS REs include TPs outside CoMPs. Thus the unionof CRS REs can be any combination of CRS RE patterns on the listincluding both TPs in the CoMP measurement set or outside the CoMPmeasurement set and/or CoMP cluster.

Now we discuss the hybrid approaches with dynamic signalling of PDSCHmapping information.

The Alt-2 as aforementioned uses a 1-bit to indicate 2 states of PDSCHmapping information which can only accommodate two CRS patterns. As themaximum size of the CoMP measurement set for a UE is 3, 1-bit is notenough to convey the CRS pattern and MBSFN sub frame information.Although with a high probability, the size of CoMP measurement set is 3,the cases of CoMP measurement set size being one cannot be neglected.Therefore, we prefer the 2-bit dynamic signalling.

We first present the following approach

Alternative 3: For CoMP JT or DPS, the network semi-statically informs aCoMP UE the CRS information and PDSCH start point for each TP in theCoMP measurement set of that UE in some order. The network then informsthe UE dynamically the PDSCH start point and CRS pattern that the PDSCHmapping will follow by conveying the indices corresponding to them.

With this approach, the network first semi-statically signals the UE theCRS information for each TP in the measurement set as in Alternative 1or Alternative 2, as well as the PDSCH starting point for each TP ifPDCCH region changes semi-statically. Then the network dynamicallysignal the index of the TP that the PDSCH mapping follows possiblyincluding the starting point. Such dynamic signal can be specified inDCI with an additional signal field. The 2-bit dynamic signal is similarto that in Table 2 except that the state for the muting on the union ofCRS REs is not necessary. If the PDSCH start points are configureddynamically on each TP in the measurement set. For this approach, theMBSFN subframe configurations are also semi-statically informed to theUE and associated to one TP or one CSI-RS resources. Also, the 2-bit DCIcan also indicate the quasi co-location assumption which is along theindicated TP or CSI-RS resource.

TABLE 3 CoMP PDSCH RE mapping indication for alternative 3. CoMP PDSCHMapping Indicator CoMP PDSCH RE Mapping 00 PDSCH mapping align to theserving cell (TP-1 in the measurement set) 01 PDSCH mapping align toTP-2 in the measurement set 10 PDSCH mapping align to TP-3 in themeasurement set 11 Reserved.

Note that the three states (00, 01, 10) in Table 3 can also be appliedto the JT with the corresponding indicated TP in non-MBSFN subframe andother TPs in their MBSFN subframe. We can use the 4^(th) state torepresent no CRS (or equivalently CRS antenna port 0) to indicate JTCoMP on MBSFN for all TPs. With this approach, the semi-staticsignalling of MBSFN subframe configuration may not be necessary becausefor any transmission on MBSFN, we can use state-11 for such indication.However, one issue for using state-11 to signal the PDSCH mapping onMBSFN subframe without semi-static information of MBSFN configuration isthat it does not support quasi-co-location indication with the 2-bitDCI.

Now the question is that if the MBSFN subframe configuration issemi-statically conveyed, whether state-11 indicating PDSCH mappingassuming no CRS is necessary or not. We think it is still useful. Forinstance, if JT is scheduled on two or three TPs and all on MBSFNsubframe, without state-11, one state of the first three states has tobe signalled to the UE, meaning that the UE has to assume thequasi-co-location along some TP. Similarly for frequency selective DPSwhere the signal may be transmitted along different TPs on the samesubframe but on different frequency resources blocks. However, for CoMPJT or frequency selective DPS, it is possible that such partialquasi-co-location indication along one TP may degrade the systemperformance. Therefore, we propose to use one state, e.g., state-11 inthe 2-bit DCI to indicate PDSCH RE mapping assuming no CRS and noquasi-co-location assumption.

Alternative 4: For PDSCH mapping in CoMP, the network semi-staticallyinforms a CoMP UE the attributes including CRS information and possiblyquasi-co-location information of each TP in its CoMP measurement set.The network then informs the UE dynamically the CRS pattern and otherattributes by conveying an index identifying them or it indicates to theUE that the PDSCH mapping will occupy all the CRS RE positions (assumingno CRS, e.g. MBSFN subframe) and that no quasi-co-location assumptionmust be made.

The dynamic signal for mapping indicator is then given in Table 4. ThePDSCH starting point and other attributes such as CRS information andquasi-co-location, etc., can be semi-statically associated to theentries of the table.

TABLE 4 CoMP PDSCH RE mapping indication for alternative 4. CoMP PDSCHMapping Indicator CoMP PDSCH RE Mapping 00 PDSCH mapping align to theserving cell (TP-1 in the measurement set) 01 PDSCH mapping align toTP-2 in the measurement set 10 PDSCH mapping align to TP-3 in themeasurement set 11 PDSCH RE mapping assuming no CRS (e.g. MBSFN) and noquasi-co-location assumption.

To semi-statically signal the CRS pattern for each TP in the UEmeasurement set using the number of CRS ports and its frequency shift(instead of cell ID), the 4-bit indices for CRS patterns are summarizedin Table 4. With this setting, the MSB b₃ of the CRS pattern indexdefines if the number of CRS port M=1 (b₃=0) or M>1 (b₃=1). If b₃=0, therest three bits (b₂b₁b₀) indicate the frequency shift. If b₃=1, the2^(nd) MSB b₂ is used to differentiate M=2 (b₂=0) or M=4 (b₂=1), thenthe rest two bits (b₁b₀) indicate the frequency shift. If the case noCRS (number of CRS port=0) is also needed to be signalled, we can useone of the reserved index, e.g., b₃b₂b₁b₀=1111, to convey thisinformation.

TABLE 5 CRS patterns. CRS pattern index Number of Frequency shift(b₃b₂b₁b₀) CRS ports of CRS 0000 1 0 0001 1 1 0010 1 2 0011 1 3 0100 1 40101 1 5 0110 Reserved Reserved 0111 Reserved Reserved 1000 2 0 1001 2 11010 2 2 1011 Reserved Reserved 1100 4 0 1101 4 1 1110 4 2 1111 ReservedReserved

One important observation is that using a common table as in Table 4 forall CoMP users, while simplifying system design, is not the best use ofsignalling resources.

For example, consider a user with a CoMP measurement set size of 2.Then, for such a user, using Table 4 would not be the optimal choicesince the entry corresponding to 10 would never be used.

Therefore, one alternative is to design a different table using 1 bitwhich covers all users with a CoMP measurement set size of 2. Since theCoMP measurement set of a user only changes semi-statically, the choiceof the table being used needs to be configured along with the CoMPmeasurement set only semi-statically.

The other alternative is to have a common size of 2 bits but to make theinterpretation of the mapping indication (i.e., the entries in thetable) to be dependent on the CoMP measurement set size. This way moreinformation can be conveyed for a user with CoMP measurement set size 2than what is possible with Table 4.

An example of this approach is the following Table 4b. Here the entry 10conveys to the user (with CoMP measurement set size 2) that PDSCHmapping for it is done assuming no CRS and also that the user shouldassume quasi co-location of TP-1. This is beneficial if MBSFNinformation of TP-1 has not been semi-statically configured for theuser. Then, when the user is scheduled to be served data by TP-1 in itsMBSFN subframe, the user can be informed using entry 10 so that the userknows that PDSCH mapping for it is done assuming no CRS and it can usethe parameters estimated during CSI-RS estimation for TP-1 to initializeits DMRS based estimator and hence achieve improved performance. Asimilar fact holds for entry 11 with respect to TP-2

TABLE 4b CoMP PDSCH RE mapping indication CoMP PDSCH Mapping IndicatorCoMP PDSCH RE Mapping 00 PDSCH mapping align to the serving cell (TP-1in the measurement set) 01 PDSCH mapping align to TP-2 in themeasurement set 10 PDSCH mapping by occupying all CRS REs in themeasurement set and Quasi Co-location of TP-1 11 PDSCH mapping byoccupying all CRS REs in the measurement set and Quasi Co-location ofTP-2

Extending this idea, suppose that the MBSFN information of TP-1 has beensemi-statically configured for the user but not that of TP-2. Then thenetwork could employ the following Table 4c

TABLE 4c CoMP PDSCH RE mapping indication CoMP PDSCH Mapping IndicatorCoMP PDSCH RE Mapping 00 PDSCH mapping align to the serving cell (TP-1in the measurement set) 01 PDSCH mapping align to TP-2 in themeasurement set 10 PDSCH mapping by occupying all CRS REs in themeasurement set and not using any Quasi Co-location 11 PDSCH mapping byoccupying all CRS REs in the measurement set and Quasi Co-location ofTP-2

Here, whenever 00 is indicated the user knows that PDSCH mapping for itis done assuming CRS of TP-1 except on the MBSFN of TP-1 when no CRS isassumed. The user now already has the ability to determine whether aframe is MBSFN for TP-1 or not. Consequently the use of entry 10 as inTable 4b is redundant. Thus, in Table 4c we use the entry 10 to informthe user that PDSCH mapping for it is done assuming no CRS and also tonot use any quasi co-location information. This covers some cases wherethe user is served by two TPs (such as in the case of joint transmission(JT) or frequency selective DPS) that have disparate quasi co-locationrelated parameters and where it is not suitable to indicate the partialquasi-co location information of one TP to a user.

Next, suppose that the MBSFN information of both TP-1 and TP-2 have beensemi-statically configured. Here an example of Table design could betable 4d

TABLE 4d CoMP PDSCH RE mapping indication CoMP PDSCH Mapping IndicatorCoMP PDSCH RE Mapping 00 PDSCH mapping align to the serving cell (TP-1in the measurement set) 01 PDSCH mapping align to TP-2 in themeasurement set 10 PDSCH mapping by occupying all CRS REs in themeasurement set and not using any Quasi Co-location 11 PDSCH mappingalign to the serving cell (TP-1 in the measurement set) and not usingany Quasi Co-location

Here, we use entry 11 to cover the case where the CRS positions of boththe TPs are identical (as in the scenario with same cell ID and withidentical number of ports for both TPs) and the user is served by bothTPs having disparate quasi co-location related parameters and it is notsuitable to indicate the partial quasi-co location information to theuser.

In a similar vein a user with CoMP set size 1 can be served using thelegacy format. Alternatively, it can be served using the DCI with 2 or 1bit dynamic indication field but where the entries in the correspondingtables are re-interpreted according to rules for CoMP measurement setsize 1.

For instance, in this case since the data serving TP is always fixed,with its CRS positions and MBSFN information already known to the user,the entries could be used to indicate PDSCH mapping assuming exclusionof the union of the CRS of the serving TP and the CRS of a stronginterferer.

Here, the assumption is that a list of interferers and some of theirattributes (such as CRS positions etc) are known via some semi-staticconfiguration mechanism between the network and the user. Consider thefollowing table.

TABLE 4e CoMP PDSCH RE mapping indication CoMP PDSCH Mapping IndicatorCoMP PDSCH RE Mapping 00 PDSCH mapping align to the serving cell (TP-1in the measurement set) 01 PDSCH mapping assuming excluding union ofTP-1 and 1^(st) strongest interferer 10 PDSCH mapping assuming excludingunion of TP-1 and 1^(st) and 2^(nd) strongest interferers 11 PDSCHmapping assuming excluding union of TP-1 and 1^(st), 2^(nd) and 3^(rd)strongest interferers

In Table 4e the entry 01 for example conveys to the user to assume PDSCHmapping excluding the RE positions covered by the union of CRS positionsof TP-1 and the 1^(st) strongest interferer. This way the user whichcannot perform CRS interference cancellation due to complexity or due toinability to accurately estimate parameters needed for suchcancellation, might be benefited since it will not try to decode data inpositions with strong interference.

Note that the indicator in Table 4e can be reduced to convey only thefirst two states if 1-bit indicator is adopted.

Finally, for each CoMP measurement set size, a codebook of tables can bedefined. Then, the choice of table from that codebook of tables that thenetwork will use can be configured in a semi-static and user specificmanner.

What is claimed is:
 1. A wireless communications method implemented in anetwork system that supports coordinated multipoint transmission andreception (CoMP), the wireless communications method comprising:informing a user equipment (UE) semi-statically of a codebook subset foreach channel state information (CSI) process, wherein the UE isrestricted to report an indication of a precoding matrix within thecodebook subset.
 2. The wireless communications method as in claim 1,wherein the indication is a PMI (precoding matrix index).
 3. Thewireless communications method as in claim 1, wherein the CSI process isassociated with a choice of a transmission points (TP) in a CoMP set. 4.The wireless communications method as in claim 3, wherein the CoMP setcomprises a CoMP measurement set.
 5. The wireless communications methodas in claim 1, wherein the method is implemented in a networkcontroller.
 6. A wireless communications method implemented in a userequipment (UE) used in network system that supports coordinatedmultipoint transmission and reception (CoMP), the wirelesscommunications method comprising: semi-statically receiving a codebooksubset for each channel state information (CSI) process, wherein the UEis restricted to report an indication of a precoding matrix within thecodebook subset.
 7. The wireless communications method as in claim 6,wherein the indication is a PMI (precoding matrix index).
 8. Thewireless communications method as in claim 6, wherein the CSI process isassociated with a choice of a transmission points (TP) in a CoMP set. 9.The wireless communications method as in claim 8, wherein the CoMP setcomprises a CoMP measurement set.
 10. A wireless communications systemthat supports coordinated multipoint transmission and reception (CoMP),the wireless communications system comprising: a user equipment (UE); anetwork controller to inform the user equipment (UE) semi-statically ofa codebook subset for each channel state information (CSI) process,wherein the UE is restricted to report an indication of a precodingmatrix within the codebook subset.
 11. The wireless communicationssystem as in claim 10, wherein the indication is a PMI (precoding matrixindex).
 12. The wireless communications system as in claim 10, whereinthe CSI process is associated with a choice of a transmission points(TP) in a CoMP set.
 13. The wireless communications system as in claim12, wherein the CoMP set comprises a CoMP measurement set.
 14. A userequipment (UE) used in network system that supports coordinatedmultipoint transmission and reception (CoMP), the user equipment (UE)comprising: a receiver to semi-statically receive a codebook subset foreach channel state information (CSI) process, wherein the UE isrestricted to report an indication of a precoding matrix within thecodebook subset.
 15. The user equipment (UE) as in claim 14, wherein theindication is a PMI (precoding matrix index).
 16. The user equipment(UE) as in claim 14, wherein the CSI process is associated with a choiceof a transmission points (TP) in a CoMP set.
 17. The user equipment (UE)as in claim 16, wherein the CoMP set comprises a CoMP measurement set.